Cracking The Ap Calculus ab Exam 2018

Here    we  will    find    the derivative  using   the Chain   Rule.   We  will    also    need    the Quotient    Rule    to

take    the derivative  of  the expression  inside  the parentheses.    The Chain   Rule    says    that    if  y   =

f(g(x)),    then    y′  =    ,  and the Quotient    Rule    says    that    if  f(x)    =    ,   then   f′(x)    =  

. We get f′(x) = 3 . This can be simplified to f′(x) =

.

5.

Here    we  will    find    the derivative  using   the Chain   Rule.   We  will    also    need    the Quotient    Rule    to

take    the derivative  of  the expression  inside  the parentheses.    The Chain   Rule    says    that    if  y   =

f(g(x)),    then    y′  =    ,  and the Quotient    Rule    says    that    if  f(x)    =    ,  then    f′(x)    =  

. We get f′(x) = . This can be simplified to f′(x) =

.

6.

We  have    two ways    that    we  could   solve   this.   We  could   expand  the expression  first   and then    take

the derivative  of  each    term,   or  we  could   find    the derivative  using   the Product Rule.   Let’s   do

both    methods just    to  see that    they    both    give    us  the same    answer. First,  let’s   use the Product

Rule,   which   says    that    if  f(x)    =   uv, then    f′(x)   =   u . Here    f(x)    =    ,  so  u

=       and v   =    .  Using   the Product Rule,   we  get f′(x)   =       +   

    =       +    .  This    can be  simplified  to  f′(x)

= + = .

The other   way we  could   find    the derivative  is  to  expand  the expression  first   and then    take    the