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Example Questions
Example Question #41 : First And Second Derivatives Of Functions
Find the velocity given the displacement function
The derivative of the displacement function is the velocity, so we need to find . We can use the power rule
with
to get
Example Question #41 : First And Second Derivatives Of Functions
Find the velocity given the displacement function
The derivative of the displacement function is the velocity, so we need to find . We can use the power rule
with along with the chain rule to get
Example Question #43 : First And Second Derivatives Of Functions
Find the velocity given the displacement function
The derivative of the displacement function is the velocity, so we need to find . We can use the power rule
with along with the chain rule to get
Example Question #42 : First And Second Derivatives Of Functions
Find the velocity given the displacement function
The derivative of the displacement function is the velocity, so we need to find . We can use the power rule
with along with the chain rule to get
Example Question #45 : First And Second Derivatives Of Functions
Given the displacement function , find the velocity function.
To find the velocity of , we need to find the derivative. This can be done with the chain rule:
with and , so we get
and
so we get
Example Question #43 : First And Second Derivatives Of Functions
Given the displacement function , find the velocity function.
To find the velocity of , we need to find the derivative. This can be done with the chain rule:
with and , so we get
and
so we get
Example Question #241 : Derivatives
Given the displacement function
find the velocity function.
To find the velocity of , we need to find the derivative. This is simply:
using the power rule:
Example Question #45 : First And Second Derivatives Of Functions
Given the velocity function
find the acceleration function .
The acceleration function can be derived from the velocity function by taking the derivative: . So we get
Example Question #46 : First And Second Derivatives Of Functions
Given the velocity function
find the acceleration function .
The acceleration function can be derived from the velocity function by taking the derivative: . So we get
Example Question #47 : First And Second Derivatives Of Functions
Find the derivative of
None of the other answers
We need to use the Product Rule to evaluate the derivative here.
The formula for the Product Rule is
If , , then ,
Plugging these into our formula, we get-
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