AP Calculus AB : Derivatives of functions
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Example Questions
Example Question #91 : Derivatives Of Functions
What is the second derivative of the following function?
Example Question #92 : Derivatives Of Functions
What is 
Example Question #93 : Derivatives Of Functions
What function is equivalent to the tenth derivative of the following function?
The tenth derivative is undefined.
Even though the coefficients become massive as one progresses through successive derivatives of f(x), the sixth derivative yields a constant. The following seventh derivative will therefore equal zero, as will all following derivatives. We can confidently state — without necessarily deriving the equation ten times — that the tenth derivative will result in an equation equivalent to y=0.
Example Question #93 : Derivatives Of Functions
Find
None of the other answers.
According to the chain rule:
if 
So, 
To find the second derivative, we will use the chain rule again:
Therefore, 
Finally, we simply plug in 
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