Cracking The Ap Calculus ab Exam 2018

Note:   We  refer   to  the log 10   x  as  log x.

Example 9: Find the derivative of f(x) = log 8 (x^2 + x).

f′(x)   =   

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

f′(x)   =   

You can expect this result from Rules 1 and 2 involving natural logs.

THE DERIVATIVE OF ax

You should recall from your precalculus days that we can rewrite ax as ex ln a. Keep in mind that ln a is
just a constant, which gives us the next rule.

Rule    No. 7:  If  y   =   ax, then        =   (ex ln  a)  ln  a   =   ax  (ln a)

Given the pattern of this chapter, you can guess what’s coming: another rule that incorporates the Chain
Rule.

Rule    No. 8:  If  y   =   au, then        =   (ln a)

And now, some examples.

Example 11: Find the derivative of f(x) = 3x.

f′(x)   =   3x  ln  3

Example 12: Find the derivative of f(x) = 8^4 x

5

.

f′(x)   =   8^4 x

5

    (20x^4 )    ln  8