Cracking The Ap Calculus ab Exam 2018

We  find    the derivative  of  a   function,   f(x),   using   the definition  of  the derivative, which   is  f′(x)   =   

. Here f(x) = and f(x + h) = . If we now plug these into the

definition  of  the derivative, we  get f′(x)   =       =    .  Notice  that

if  we  now take    the limit,  we  get the indeterminate   form     .  We  cannot  eliminate   this    problem

merely  by  simplifying the expression  the way that    we  did with    a   polynomial. Here    we  combine

the  two     terms   in  the     numerator   of  the     expression  to  get     f′(x)   =   =  

=    .   This    simplifies  to f′(x)    =   =  

    =    .  Now we  can cancel  the h   in  the numerator   and the denominator

to  get f′(x)   =       =    .  Now we  take    the limit:  f′(x)   =       =   

.

15. 80 x^9

Simply  use the Power   Rule.   The derivative  is  8x^10   =   8(10x^9 )   =   80x^9.

16.

Use  the     Power   Rule    to  take    the     derivative  of  each    term.   The     derivative  of 

. The derivative of . The derivative of (remember the

shortcut    that    we  showed  you on  this    page).  Therefore,  the derivative  is      =   

.

17.

Use  the     Power   Rule    to  take    the     derivative  of  each    term.   The     derivative  of