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

Question

Quizplus · Accepted Answer

Using the chain rule and the derivative of the natural logarithm function, we have:

\begin{align*}
\frac{dy}{d	heta} &= \frac{1}{\cos(\ln	heta)}\cdot\frac{d}{d	heta}\cos(\ln	heta)\
&= \frac{-\sin(\ln	heta)}{\cos(\ln	heta)\cdot	heta}\
&= -\frac{	an(\ln	heta)}{	heta}
\end{align*}

Therefore, the answer is B, $-\frac{	an(\ln	heta)}{	heta}$.

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.

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