Cracking The Ap Calculus ab Exam 2018

3. C Step 1: We need to use the Quotient Rule to evaluate this derivative. Remember, the derivative

of   .  But,    before  we  take    the derivative, we  should  factor  an  x   out of  the

top and bottom  and cancel, simplifying the quotient.

Step    2:  Now take    the derivative.

f′(x)   =   

Step    3:  Simplify.

4. B If we take the limit as x goes to 0, we get an indeterminate form , so let’s use L’Hôpital’s

Rule.    We  take    the     derivative  of  the     numerator   and     the     denominator     and     we  get:   

. Now, when we take the limit we get: =0.
5. B We need to use Implicit Differentiation to find . First, take the derivative with respect to x

of  both    sides:      =   cos(xy)  .  Remember    that    you need    to  use the Product Rule    to

find    the derivative  of  xy.

Now distribute  on  the right   side:       =   x   cos(xy  +   y   cos(xy).

Next,   group   the terms   containing      on  the left    side:       −   x   cos(xy) =   y   cos(xy).