All Calculus 2 Resources
Example Questions
Example Question #11 : First And Second Derivatives Of Functions
Find the derivative of the following function:
The derivative of the function is equal to
and was found using the following rules:
, , ,
Example Question #1 : Applications Of Derivatives
Let
Find the first and second derivative of the function.
In order to solve for the first and second derivative, we must use the chain rule.
The chain rule states that if
and
then the derivative is
In order to find the first derviative of the function
we set
and
Because the derivative of the exponential function is the exponential function itself, we get
And differentiating we use the power rule which states
As such
And so
To solve for the second derivative we set
and
Because the derivative of the exponential function is the exponential function itself, we get
And differentiating we use the power rule which states
As such
And so the second derivative becomes
Example Question #212 : Derivative Review
Find the derivative of the following function:
The derivative of the function is equal to
and was found using the following rules:
, ,
Example Question #213 : Derivative Review
Find the derivative of the function:
The integral of the function is equal to
and was found using the following rules:
,
Note that it is easier to integrate the first term once it is rewritten as .
Example Question #2 : Applications Of Derivatives
Find the velocity function of the particle if its position is given by the following function:
The velocity function is given by the first derivative of the position function:
and was found using the following rules:
, , ,
Example Question #12 : First And Second Derivatives Of Functions
Find the second derivative of the following function:
The first derivative of the function is equal to
The second derivative - the derivative of the function above - of the original function is equal to
Both derivatives were found using the following rules:
, , ,
Example Question #1341 : Calculus Ii
Find the derivative of the following function:
The derivative was found using the following rules:
, , ,
Example Question #1342 : Calculus Ii
Find the derivative of the function:
The derivative of the function is equal to
and was found using the following rules:
, , , ,
Example Question #212 : Derivatives
Find the derivative of the following function:
The derivative of the function was found using the following rules:
, , ,
Example Question #1344 : Calculus Ii
Solve for the derivative:
Write the derivative of cotangent .
The problem requires chain rule since the inner function is . The chain rule is the derivative of the inner function, and the derivative of is .
Take the derivative to obtain . Multiply the value obtained by the use of chain rule.