$$\text { Find the derivative of } y \text { with respect to } x , t , \text { or } \theta \text {, as appropriate. }$$
-$y = \ln ( \ln 2 x )$
A) $\frac { 1 } { x }$
B) $\frac { 1 } { \ln 2 x }$
C) $\frac { 1 } { x \ln 2 x }$
D) $\frac { 1 } { 2 x }$

Question

Quizplus · Accepted Answer

We use the chain rule and the derivative of the natural logarithm to find the derivative of y:
\begin{align*}
\frac{dy}{dx} &= \frac{1}{\ln(2x)} \cdot \frac{1}{2x} \cdot 2 \
&= \frac{1}{x \ln(2x)}
\end{align*}
Therefore, the correct answer is (C).

Find the derivative of y with respect to x,t, or θ, as appropriate. \text { Find the derivative of } y \text { with respect to } x , t , \text { or } \theta \text {, as appropriate. } Find the derivative of y with respect to x,t, or θ, as appropriate.

$\text { Find the derivative of } y \text { with respect to } x , t , \text { or } \theta \text {, as appropriate. }$