All AP Calculus AB Resources
Example Questions
Example Question #63 : Ap Calculus Ab
Find the derivative.
Use the power rule to find the derivative.
Example Question #64 : Ap Calculus Ab
Find the derivative.
The derivative of is . (Memorization)
Example Question #65 : Ap Calculus Ab
Find the derivative.
Use the chain rule to find the derivative:
Thus, .
Example Question #66 : Ap Calculus Ab
Find the derivative.
Use the power rule to find the derivative.
The derivative of a constant is zero.
Thus, the derivative is .
Example Question #71 : Ap Calculus Ab
Use the method of your choice to find the derivative.
The easiest way to find this derivative is to FOIL, and then use the power rule.
Example Question #72 : Ap Calculus Ab
Find the derivative.
Use the product rule to find this derivative.
Example Question #71 : Derivatives
Define
Evaluate and so that is both continuous and differentiable at .
For to be continuous at , it must hold that
.
To find , we can use the definition of for all negative values of :
It must hold that as well; using the definition of for all positive values of :
.
Therefore, .
Now examine . For to be differentiable, it must hold that
To find , we can differentiate the expression for for all negative values of :
Again, through straightforward substitution,
To find , we can differentiate the expression for for all positive values of :
Again, through substitution,
and .
Example Question #73 : Ap Calculus Ab
Find the derivative.
Use the power rule to find the derivative.
Thus, the derivative is
Example Question #74 : Ap Calculus Ab
Find the derivative.
Use the quotient rule to find the derivative.
Simplify.
Example Question #51 : Derivatives Of Functions
Find the first derivative of the function:
The derivative of the function is equal to
and was found using the following rules:
, , ,
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