All GRE Subject Test: Math Resources
Example Questions
Example Question #1 : Derivatives & Integrals
Find :
Write the quotient rule.
For the function ,
and
,
and
.
Substitute and solve for the derivative.
Reduce the first term.
Example Question #1 : Derivatives & Integrals
Find the following derivative:
Given
This question asks us to find the derivative of a quotient. Use the quotient rule:
Start by finding and
.
So we get:
Whew, let's simplify
Example Question #1 : Finding Derivatives
Find derivative .
This question yields to application of the quotient rule:
So find and
to start:
So our answer is:
Example Question #11 : Derivatives & Integrals
Find the derivative of: .
None of the Above
Step 1: We need to define the quotient rule. The quotient rule says: , where
is the derivative of
and
is the derivative of
Step 2: We need to review how to take derivatives of different kinds of terms. When we are taking the derivative of terms in a polynomial, we need to follow these rules:
Rule 1: For any term with an exponent, the derivative of that term says: Drop the exponent and multiply it to the coefficient of that term. The new exponent of the derivative is lower than the previous exponent.
Example:
Rule 2: For any term in the form , the derivative of that term is just
, the coefficient of that term.
Ecample:
Rule 3: The derivative of any constant is always
Step 3: Find and
:
Step 4: Plug in all equations into the quotient rule:
Step 5: Simplify the fraction in step 4:
Step 6: Combine terms in the numerator in step 5:.
The derivative of is
Example Question #1 : Quotient Rule
Find the derivative of:
Step 1: Define .
Step 2: Find .
Step 3: Plug in the functions/values into the formula for quotient rule:
The derivative of the expression is
Example Question #3 : Quotient Rule
Find derivative .
This question yields to application of the quotient rule:
So find and
to start:
So our answer is:
Example Question #1 : Quotient Rule
Find the second derivative of:
None of the Above
None of the Above
Finding the First Derivative:
Step 1: Define
Step 2: Find
Step 3: Plug in all equations into the quotient rule formula:
Step 4: Simplify the fraction in step 3:
Step 5: Factor an out from the numerator and denominator. Simplify the fraction..
We have found the first derivative..
Finding Second Derivative:
Step 6: Find from the first derivative function
Step 7: Find
Step 8: Plug in the expressions into the quotient rule formula:
Step 9: Simplify:
I put "..." because the numerator is very long. I don't want to write all the terms...
Step 10: Combine like terms:
Step 11: Factor out and simplify:
Final Answer: .
This is the second derivative.
The answer is None of the Above. The second derivative is not in the answers...
All GRE Subject Test: Math Resources
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