Calculus 2 : First and Second Derivatives of Functions
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Example Questions
Example Question #1571 : Calculus Ii
What is the derivative of 
Recall that when taking the derivative, multiply the exponent by the coefficient in front of the x term and then also subtract one from the exponent:
Recall that the derivative of a constant is just zero.
Example Question #451 : Derivatives
What is the second derivative of 
Before you can take the second derivative, you must first take the first derivative. Remember to multiply the exponent by the coefficient in front of the x term and then subtract one from the exponent:
Now, take the second derivative:
Example Question #253 : First And Second Derivatives Of Functions
Find the first and second derivative of the function.
To find the first and second derivatives, we use the chain rule.
where 
For the first derivative we have 
For the second derivative we have 
Example Question #254 : First And Second Derivatives Of Functions
Find the first and second derivative of the function.
We find the first derivative by deriving term by term. As such,
Taking the second derivative
Example Question #255 : First And Second Derivatives Of Functions
What is the first derivative of
To find the first derivative, look at each term separately.
For the first term, multiply the exponent by the coefficient (
Do the same with the next term: 
For the third term, the derivative is just the coefficient (1 in this case).
The derivative of a constant is 0.
Put those all together to get your answer: 
Example Question #256 : First And Second Derivatives Of Functions
Find the second derivative of 
Before finding the second derivative, you must find the first derivative. Remember to multiply the exponent by the coefficient and then subtract one from the exponent. Evaluate each term separately and then put all together at the end.
The first derivative is: 
Now, take the derivative of the 1st derivative to find the second derivative:
Example Question #257 : First And Second Derivatives Of Functions
Find the first derivative of 
First, chop up the fraction into 2 separate terms and simplify:
Now, take the derivative of that expression. Remember to multiply the exponent by the coefficient and then decrease the exponent by 1:
Example Question #258 : First And Second Derivatives Of Functions
Integrate each term separately. When there is just an x on the denominator, the integral of that is 
Therefore, the first term integrated is:
The second term integrated is:
Put those together to get:
Because it's an indefinite integral, remember to add C at the end:
Example Question #4 : Velocity, Speed, Acceleration
Given the velocity function
where 
We can find the acceleration function 
We can view the function
as the composition of the following functions
so that 
to find the derivative. We have 
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