Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Finding Derivatives

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Finding Derivative At A Point

Find $f^{'}(2)$ if the function f(x) is given by

f(x) = ln(x)

Possible Answers:

$\frac{1}{2}$

$\frac{3}{2}$

Correct answer:

$\frac{1}{2}$

Explanation:

To find the derivative at x=2 , we first take the derivative of f(x) . By the derivative rule for logarithms,

$f'(x) = \frac{1}{x}$

Plugging in x=2 , we get

$f'(2) = \frac{1}{2}$

Report an Error

Example Question #1 : Finding Derivatives

Find the derivative of the following function at the point x=3 .

f(x) = 4x^3+x+3

Possible Answers:

109

110

108

107

106

Correct answer:

109

Explanation:

Use the power rule on each term of the polynomial to get the derivative,

f'(x) = (3)(4)x^2+1

Now we plug in x=3

f'(3) = (12)(3)^2 + 1 = 109

Report an Error

Example Question #2 : Finding Derivatives

Let $f(x)=x^2\sin(x^2)$ . What is $f'\left (\frac{\sqrt{\pi}}{2} \right )$ ?

Possible Answers:

$\frac{\sqrt{2\pi}(\pi + \sqrt{2})}{4}$

$\frac{\sqrt{2\pi}(\pi + 4)}{8}$

$\frac{{2\pi}(\sqrt{\pi} + 2)}{4}$

$\frac{\sqrt{2\pi}(\pi + 2)}{4}$

$\frac{(\pi + \sqrt{2})}{8}$

Correct answer:

$\frac{\sqrt{2\pi}(\pi + 4)}{8}$

Explanation:

We need to find the first derivative of f(x). This will require us to apply both the Product and Chain Rules. When we apply the Product Rule, we obtain:

$f'(x)=\sin(x^2)\cdot\frac{\mathrm{d} }{\mathrm{d} x}[x^2]+x^2\cdot\frac{\mathrm{d} }{\mathrm{d} x}[\sin(x^2)]$

In order to find the derivative of $\sin(x^2)$ , we will need to employ the Chain Rule.

$\frac{\mathrm{d} }{\mathrm{d} x}[\sin(x^2)]=\cos(x^2)\cdot\frac{\mathrm{d} }{\mathrm{d} x}[x^2]=\cos(x^2)\cdot2x$

$f'(x)=\sin(x^2)\cdot2x + x^2\cdot\cos(x^2)\cdot2x$

We can factor out a 2x to make this a little nicer to look at.

$f'(x)=2x(\sin(x^2)+x^2\cos(x^2))$

Now we must evaluate the derivative when x = $\frac{\sqrt{\pi}}{2}$ .

$f'\left (\frac{\sqrt{\pi}}{2} \right )=2\cdot\frac{\sqrt{\pi}}{2}(\sin\frac{\pi}{4}+\frac{\pi}{4}\cos\frac{\pi}{4})$

$=\sqrt{\pi}(\frac{\sqrt{2}}{2}+\frac{\pi\sqrt{2}}{8})=\sqrt{2\pi}(\frac{1}{2}+\frac{\pi}{8})=\frac{\sqrt{2\pi}(\pi + 4)}{8}$

The answer is $\frac{\sqrt{2\pi}(\pi + 4)}{8}$ .

Report an Error

Example Question #2094 : High School Math

What is the first derivative of $4x^2+\frac{2}{3}x$ ?

Possible Answers:

$8\tfrac{2}{3}x^2$

$8x+\frac{2}{3}$

Correct answer:

$8x+\frac{2}{3}$

Explanation:

To find the first derivative for this problem, we can use the power rule. The power rule states that we lower the exponent of each of the variables by one and multiply by that original exponent.

$\frac{\mathrm{d} }{\mathrm{d} x}(4x^2+\frac{2}{3}x)=(2*4x^{2-1})+(1*\frac{2}{3}x^{1-1})$

$\frac{\mathrm{d} }{\mathrm{d} x}(4x^2+\frac{2}{3}x)=(2*4x^{1})+(1*\frac{2}{3}x^{0})$

Remember that anything to the zero power is one.

$\frac{\mathrm{d} }{\mathrm{d} x}(4x^2+\frac{2}{3}x)=(8x)+(1*\frac{2}{3}(1))$

$\frac{\mathrm{d} }{\mathrm{d} x}(4x^2+\frac{2}{3}x)=8x+\frac{2}{3}$

Report an Error

Example Question #1 : Finding Derivative Of A Function

$\frac{\mathrm{d} }{\mathrm{d} x}(4x^2+5x-3)=?$

Possible Answers:

8x+5

16x+5

8x-8

Correct answer:

8x+5

Explanation:

This problem is best solved by using the power rule. For each variable, multiply by the exponent and reduce the exponent by one:

$\frac{\mathrm{d} }{\mathrm{d} x}(4x^2+5x-3)=(2*4x^{2-1})+(1*5x^{1-1})-(0*3x^0-1)$

Treat as 3x^0 since anything to the zero power is one.

Remember, anything times zero is zero.

$\frac{\mathrm{d} }{\mathrm{d} x}(4x^2+5x-3)=(8x^{1})+(5x^{0})-0$

$\frac{\mathrm{d} }{\mathrm{d} x}(4x^2+5x-3)=8x+5$

Report an Error

Example Question #3 : Finding Derivatives

Give the average rate of change of the function $f(x) = 4 ^{x}$ on the interval [3,4] .

Possible Answers:

256

192

Correct answer:

192

Explanation:

The average rate of change of on interval [a,b] is

$\frac{f (b ) - f(a)}{b-a}$

Substitute:

$\frac{f (4 ) - f(3)}{4-3} = \frac{4^{4} - 4^{3}}{1} = \frac{256 - 64}{1} = 192$

Report an Error

Example Question #4 : Finding Derivatives

What is the derivative of x^2+5x ?

Possible Answers:

x^2

$\frac{1}{2}x+5$

2x+5

$\frac{1}{3}x^3+\frac{5}{2}x^2+c$

Correct answer:

2x+5

Explanation:

To solve this problem, we can use the power rule. That means we lower the exponent of the variable by one and multiply the variable by that original exponent.

$\frac{\mathrm{d} }{\mathrm{d} x}(x^2+5x)=(2*x^{2-1})+(1*5x^{1-0})$

$\frac{\mathrm{d} }{\mathrm{d} x}(x^2+5x)=2x+5x^0$

Remember that anything to the zero power is one.

$\frac{\mathrm{d} }{\mathrm{d} x}(x^2+5x)=2x+5*1$

$\frac{\mathrm{d} }{\mathrm{d} x}(x^2+5x)=2x+5$

Report an Error

Example Question #2 : Finding Derivative Of A Function

What is the derivative of 5x+8 ?

Possible Answers:

5x^2+8x+c

$\frac{5}{2}x^2+8x$

Correct answer:

Explanation:

To solve this problem, we can use the power rule. That means we lower the exponent of the variable by one and multiply the variable by that original exponent.

We're going to treat as 8x^0 , as anything to the zero power is one.

That means this problem will look like this:

$\frac{\mathrm{d} }{\mathrm{d} x}(5x+8)=(5*x^{1-1})+(0*8x^{0-1})$

Notice that $(0*8x^{0-1})=0$ , as anything times zero is zero.

$\frac{\mathrm{d} }{\mathrm{d} x}(5x+8)=(5*x^{1-1})$

$\frac{\mathrm{d} }{\mathrm{d} x}(5x+8)=(5*x^{0})$

Remember, anything to the zero power is one.

$\frac{\mathrm{d} }{\mathrm{d} x}(5x+8)=5*1$

$\frac{\mathrm{d} }{\mathrm{d} x}(5x+8)=5$

Report an Error

Example Question #5 : Finding Derivatives

What is the derivative of x^3+2x+5 ?

Possible Answers:

3x^2+2

3x^2+2x

$\frac{1}{3}x^2+\frac{1}{2}x+\frac{1}{5}$

Correct answer:

3x^2+2

Explanation:

To solve this problem, we can use the power rule. That means we lower the exponent of the variable by one and multiply the variable by that original exponent.

We're going to treat as 5x^0 , as anything to the zero power is one.

$\frac{\mathrm{d} }{\mathrm{d} x}(x^3+2x+5)=(3*x^{3-1})+(1*2x^{1-1})+(0*5x^{0-1})$

Notice that $(0*5x^{0-1})=0$ , as anything times zero is zero.

$\frac{\mathrm{d} }{\mathrm{d} x}(x^3+2x+5)=(3*x^{3-1})+(1*2x^{1-1})$

$\frac{\mathrm{d} }{\mathrm{d} x}(x^3+2x+5)=(3*x^{2})+(2x^{0})$

$\frac{\mathrm{d} }{\mathrm{d} x}(x^3+2x+5)=3x^2+2$

Report an Error

Example Question #6 : General Derivatives And Rules

What is the derivative of ?

Possible Answers:

$\frac{3}{2}x$

$\frac{2}{3}x^3+c$

2+c

Correct answer:

Explanation:

To get $\frac{\mathrm{d} }{\mathrm{d} x}(2x)$ , we can use the power rule.

Since the exponent of the is , as 2x=2x^1 , we lower the exponent by one and then multiply the coefficient by that original exponent:

$\frac{\mathrm{d} }{\mathrm{d} x}(2x)=1*2x^{1-1}$

$\frac{\mathrm{d} }{\mathrm{d} x}(2x)=2x^{0}$

Anything to the power is .

$\frac{\mathrm{d} }{\mathrm{d} x}(2x)=2*1$

$\frac{\mathrm{d} }{\mathrm{d} x}(2x)=2$

Report an Error

View Tutors

Benjamin
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Computer Science.

View Tutors

Kurosh
Certified Tutor

University of tehran, Bachelor of Engineering, Electrical Engineering.

View Tutors

Jacqueline
Certified Tutor

University of North Carolina at Asheville, Bachelor in Arts, Mathematics. Western Carolina University, Doctor of Education, E...

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Statistics Tutors in Phoenix, Spanish Tutors in San Diego, LSAT Tutors in Seattle, Math Tutors in Houston, Computer Science Tutors in Denver, Chemistry Tutors in Los Angeles, English Tutors in San Diego, GRE Tutors in Chicago, English Tutors in Seattle, Statistics Tutors in Houston

Popular Courses & Classes

LSAT Courses & Classes in Boston, ISEE Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Denver, Spanish Courses & Classes in Houston, SSAT Courses & Classes in Chicago, MCAT Courses & Classes in Philadelphia, ISEE Courses & Classes in Seattle, Spanish Courses & Classes in Denver

Popular Test Prep

LSAT Test Prep in Denver, SAT Test Prep in Chicago, GMAT Test Prep in Philadelphia, LSAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Denver, SAT Test Prep in San Francisco-Bay Area, GRE Test Prep in San Diego, SAT Test Prep in Phoenix, ISEE Test Prep in Phoenix, ACT Test Prep in Los Angeles

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

High School Math : Finding Derivatives

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Finding Derivative At A Point

Example Question #1 : Finding Derivatives

Example Question #2 : Finding Derivatives

Example Question #2094 : High School Math

Example Question #1 : Finding Derivative Of A Function

Example Question #3 : Finding Derivatives

Example Question #4 : Finding Derivatives

Example Question #2 : Finding Derivative Of A Function

Example Question #5 : Finding Derivatives

Example Question #6 : General Derivatives And Rules

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: