All Calculus 3 Resources
Example Questions
Example Question #1 : Gradient Vector, Tangent Planes, And Normal Lines
Find the equation of the tangent plane to at .
First, we need to find the partial derivatives in respect to , and , and plug in .
,
,
,
Remember that the general equation for a tangent plane is as follows:
Now lets apply this to our problem
Example Question #21 : Applications Of Partial Derivatives
Find the slope of the function at the point
To consider finding the slope, let's discuss the topic of the gradient.
For a function , the gradient is the sum of the derivatives with respect to each variable, multiplied by a directional vector:
It is essentially the slope of a multi-dimensional function at any given point
Knowledge of the following derivative rules will be necessary:
Trigonometric derivative:
Note that u may represent large functions, and not just individual variables!
The approach to take with this problem is to simply take the derivatives one at a time. When deriving for one particular variable, treat the other variables as constant.
Looking at at the point
x:
y:
z:
Example Question #2 : Gradient Vector, Tangent Planes, And Normal Lines
Find the slope of the function at the point
To consider finding the slope, let's discuss the topic of the gradient.
For a function , the gradient is the sum of the derivatives with respect to each variable, multiplied by a directional vector:
It is essentially the slope of a multi-dimensional function at any given point
Knowledge of the following derivative rules will be necessary:
Trigonometric derivative:
Note that u may represent large functions, and not just individual variables!
The approach to take with this problem is to simply take the derivatives one at a time. When deriving for one particular variable, treat the other variables as constant.
Looking at at the point
x:
y:
z:
Example Question #1 : Gradient Vector, Tangent Planes, And Normal Lines
Find the slope of the function at the point
To consider finding the slope, let's discuss the topic of the gradient.
For a function , the gradient is the sum of the derivatives with respect to each variable, multiplied by a directional vector:
It is essentially the slope of a multi-dimensional function at any given point
The approach to take with this problem is to simply take the derivatives one at a time. When deriving for one particular variable, treat the other variables as constant.
Looking at at the point
x:
y:
z:
Example Question #2 : Gradient Vector, Tangent Planes, And Normal Lines
Find the slope of the function at the point
To consider finding the slope, let's discuss the topic of the gradient.
For a function , the gradient is the sum of the derivatives with respect to each variable, multiplied by a directional vector:
It is essentially the slope of a multi-dimensional function at any given point.
The approach to take with this problem is to simply take the derivatives one at a time. When deriving for one particular variable, treat the other variables as constant.
Looking at at the point
x:
y:
z:
Example Question #3 : Gradient Vector, Tangent Planes, And Normal Lines
Find the slope of the function at the point
To consider finding the slope, let's discuss the topic of the gradient.
For a function , the gradient is the sum of the derivatives with respect to each variable, multiplied by a directional vector:
It is essentially the slope of a multi-dimensional function at any given point.
The approach to take with this problem is to simply take the derivatives one at a time. When deriving for one particular variable, treat the other variables as constant.
Looking at at the point
x:
y:
z:
Example Question #6 : Gradient Vector, Tangent Planes, And Normal Lines
Find the slope of the function at the point
To consider finding the slope, let's discuss the topic of the gradient.
For a function , the gradient is the sum of the derivatives with respect to each variable, multiplied by a directional vector:
It is essentially the slope of a multi-dimensional function at any given point.
The approach to take with this problem is to simply take the derivatives one at a time. When deriving for one particular variable, treat the other variables as constant.
Looking at at the point
x:
y:
z:
Example Question #7 : Gradient Vector, Tangent Planes, And Normal Lines
Find the slope of the function at the point
To consider finding the slope, let's discuss the topic of the gradient.
For a function , the gradient is the sum of the derivatives with respect to each variable, multiplied by a directional vector:
It is essentially the slope of a multi-dimensional function at any given point.
The approach to take with this problem is to simply take the derivatives one at a time. When deriving for one particular variable, treat the other variables as constant.
Looking at at the point
x:
y:
Example Question #1561 : Calculus 3
Find the slope of the function at the point
To consider finding the slope, let's discuss the topic of the gradient.
For a function , the gradient is the sum of the derivatives with respect to each variable, multiplied by a directional vector:
It is essentially the slope of a multi-dimensional function at any given point.
The approach to take with this problem is to simply take the derivatives one at a time. When deriving for one particular variable, treat the other variables as constant.
Looking at at the point
x:
y:
Example Question #4 : Gradient Vector, Tangent Planes, And Normal Lines
Find the slope of the function at the point
To consider finding the slope, let's discuss the topic of the gradient.
For a function , the gradient is the sum of the derivatives with respect to each variable, multiplied by a directional vector:
It is essentially the slope of a multi-dimensional function at any given point.
The approach to take with this problem is to simply take the derivatives one at a time. When deriving for one particular variable, treat the other variables as constant.
Looking at at the point
x:
y:
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