Find the derivative of y.
-$$y = \ln ( \operatorname { sech } ( 7 x + 9 ) )$$
A) $\frac { 7 } { \operatorname { sech } ( 7 x + 9 ) }$
B) $\tanh ( 7 x + 9 )$
C) $- \tanh ( 7 x + 9 )$
D) $- 7 \tanh ( 7 x + 9 )$

Question

Quizplus · Accepted Answer

We use chain rule and derivative of natural logarithm to find the derivative of y as follows:

\begin{align*}
y &= \ln ( \operatorname { sech } ( 7 x + 9 ) )\
\frac{dy}{dx} &= \frac{1}{\operatorname { sech } ( 7 x + 9 ) } \cdot \frac{d}{dx} \operatorname { sech } ( 7 x + 9 )\
&= \frac{1}{\operatorname { sech } ( 7 x + 9 ) } \cdot (-\operatorname{sech} (7x+9)	anh(7x+9)\cdot 7)\
&= -7 	anh(7x+9)\
\end{align*}

Therefore, the correct answer is D.

Find the Derivative of Y y=ln⁡(sech⁡(7x+9))y = \ln ( \operatorname { sech } ( 7 x + 9 ) )y=ln(sech(7x+9))

Find the Derivative of Y $y = \ln ( \operatorname { sech } ( 7 x + 9 ) )$