Let $f ( x ) = \log _ { 3 } x ^ { 2 }$ . Find the value of $f ^ { \prime } ( 2 )$ .
A) $3 ^ { e }$
B)ln 3
C)ln $\left( \frac { 1 } { 3 } \right)$
D)1
E) $\frac { 1 } { \sqrt { 3 } }$
F) $\frac { 1 } { \ln 3 }$
G)
$\frac { 1 } { 3 }$
H) $\sqrt { 3 }$

Question

Let $f ( x ) = \log _ { 3 } x ^ { 2 }$ . Find the value of $f ^ { \prime } ( 2 )$ .
A) $3 ^ { e }$
B)ln 3
C)ln $\left( \frac { 1 } { 3 } \right)$
D)1
E) $\frac { 1 } { \sqrt { 3 } }$
F) $\frac { 1 } { \ln 3 }$
G)
$\frac { 1 } { 3 }$ 
H) $\sqrt { 3 }$

Quizplus · Accepted Answer

The derivative of $f(x) = \log_{3}(x^2)$ is $f'(x) = \frac{2}{x \ln 3}$. Evaluating at $x = 2$, $f'(2) = \frac{2}{2 \ln 3} = \frac{1}{\ln 3}$.

Let f(x)=log⁡3x2f ( x ) = \log _ { 3 } x ^ { 2 }f(x)=log3​x2

Let $f ( x ) = \log _ { 3 } x ^ { 2 }$