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Example Questions
Example Question #1491 : Calculus
Find the slope of the tangent line at
.
Begin by finding the derivative using the product rule.
The product rule is,
.
Applying this rule to our function where
we get,
Now, substitute 11 for x.
Example Question #461 : Functions
Find the slope of the tangent line at
.
Begin by finding the derivative using the product rule.
The product rule is,
.
Applying this rule to our function where
we get,
Now, substitute 1 for x.
Example Question #461 : Functions
What is the slope of the tanget line at
?
First, find the derivative using the power rule which states,
.Applying the power rule to each term in the function we get,
Now, plug in 2.5 for x.
Example Question #281 : Other Differential Functions
Find the slope of the tangent line at
.
First, find the derivative using the quotient rule which states,
.
In this particular case,
.
Therefore the derivative becomes,
Now, substitute 1.5 for x.
Example Question #281 : Other Differential Functions
Find the derivative.
Use the quotient rule to find the derivative which states,
.
In this particular case,
.
Therefore the derivative becomes,
Example Question #1501 : Calculus
Find the derivative.
Use the quotient rule to find the derivative which states,
.
In this particular case,
.
Therefore, the derivative becomes,
Example Question #287 : Other Differential Functions
What is the slope of the function
at ?
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 rule will be necessary:
Derivative of an exponential:
Note that
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.
Take the partial derivatives of
at:
:
The slope is
Example Question #288 : Other Differential Functions
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:
Derivative of an exponential:
Product rule:
Note that
and 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.
Find the partial derivatives of
at the point:
:
The slope is
Example Question #289 : Other Differential Functions
Find the slope of the function
at .
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:
Derivative of an exponential:
Note that
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.
Take the partial derivatives of
at:
:
The slope is
Example Question #290 : Other Differential Functions
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 rule will be necessary:
Derivative of an exponential:
Note that
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.
Take the partial derivative of
at the point:
:
:
The slope is
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