Cracking The Ap Calculus ab Exam 2018

5. −1

We   take    the     derivative  of  each    term    with    respect     to  x:  +  

+ = 0.

Next,   because     =   1,  we  can eliminate   that    term    to  get     +   sin y   +   y   cosx    +   (sin    x)

=    0.  Next,   don’t   simplify.   Plug    in  for     x   and     y:  +  

    +       =   0,  which   simplifies  to      +   

+       =   0.  If  we  multiply    through by   ,  we  get     =   0.

Finally,    we  can solve   for     =   −1.

6.

We  take    the derivative  of  each    term    with    respect to  x:  (2x)    +   (8y)    =   0.

Next,   because     =   1,  we  can eliminate   that    term    to  get 2x  +   (8y)    =   0.  Next,   we  can

isolate  .   Now,    we  take    the     derivative  again:  =  

. Next, because = 1 and = , we get

. This can be simplified to = .

7.

We  take    the derivative  of  each    term    with    respect to  x:      =   .

Next,   because     =   1,  we  can eliminate   that    term    to  get cos x   =   (−sin   y) .    Next,   we  can