Cracking The Ap Calculus ab Exam 2018

f′(x)   =   (sec^2 x)etanx

Example 7: Find the second derivative of f (x) = ex

2

.

f′(x)   =   2xex

2

f′′(x)  =   2   ex

2

    +   4x^2 ex

2

Once again, it’s just a matter of following a formula.

THE DERIVATIVE OF loga x

This derivative is actually a little trickier than the derivative of a natural log. First, if you remember your
logarithm rules about change of base, we can rewrite loga x.

loga x  =   

Review the unit on Prerequisite Mathematics if this leaves you scratching your head. Anyway, because ln
a is a constant, we can take the derivative.

This leads us to our next rule.

Rule    No. 5:  If  y   =   logax,  then    

Once again, incorporating the Chain Rule gives us a more useful formula.

Rule    No. 6:  If  y   =   logau,  then    

Example 8: Find the derivative of f(x) = log 10 x.

f′(x)   =