ap-calculus-ab 2012 Q14

ap-calculus-ab · Usa · practice-exam Chain Rule Chain Rule with Composition of Explicit Functions
If $f ( x ) = \sqrt { x ^ { 2 } - 4 }$ and $g ( x ) = 3 x - 2$, then the derivative of $f ( g ( x ) )$ at $x = 3$ is
(A) $\frac { 7 } { \sqrt { 5 } }$
(B) $\frac { 14 } { \sqrt { 5 } }$
(C) $\frac { 18 } { \sqrt { 5 } }$
(D) $\frac { 15 } { \sqrt { 21 } }$
(E) $\frac { 30 } { \sqrt { 21 } }$
If $f ( x ) = \sqrt { x ^ { 2 } - 4 }$ and $g ( x ) = 3 x - 2$, then the derivative of $f ( g ( x ) )$ at $x = 3$ is

(A) $\frac { 7 } { \sqrt { 5 } }$

(B) $\frac { 14 } { \sqrt { 5 } }$

(C) $\frac { 18 } { \sqrt { 5 } }$

(D) $\frac { 15 } { \sqrt { 21 } }$

(E) $\frac { 30 } { \sqrt { 21 } }$