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 ofis. (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 #73 :Derivatives
Define
Evaluateandso thatis both continuous and differentiable at.
Forto be continuous at, it must hold that
.
To find, we can use the definition offor all negative values of:
It must hold thatas well; using the definition offor all positive values of:
.
Therefore,.
Now examine. Forto be differentiable, it must hold that
To find, we can differentiate the expression forfor all negative values of:
Again, through straightforward substitution,
To find, we can differentiate the expression forfor 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 #76 :Derivatives
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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