Find the derivative of y with respect to x.
-$$y = - \cos ^ { - 1 } \left( \frac { 6 x + 3 } { 9 } \right)$$
A) $- \frac { 6 } { \sqrt { 81 - ( 6 x + 3 ) ^ { 2 } } }$
B) $\frac { 6 } { \sqrt { 81 - ( 6 x + 3 ) ^ { 2 } } }$
C) $\frac { 54 } { \sqrt { 1 + ( 6 x + 3 ) ^ { 2 } } }$
D) $\frac { 6 } { 1 + ( 6 x + 3 ) ^ { 2 } }$

Question

Quizplus · Accepted Answer

Using the chain rule, we have

\begin{align*}
\frac{d}{dx}\left[-\cos^{-1}\left(\frac{6x+3}{9}ight)ight] &= -\frac{1}{\sqrt{1-\left(\frac{6x+3}{9}ight)^2}}\cdot\frac{d}{dx}\left[\frac{6x+3}{9}ight] \
&= -\frac{1}{\sqrt{81-(6x+3)^2}}\cdot\left(\frac{6}{9}ight) \
&= -\frac{6}{9\sqrt{81-(6x+3)^2}} \
&= -\frac{2}{3\sqrt{81-(6x+3)^2}} \
&= \frac{6}{\sqrt{81-(6x+3)^2}}.
\end{align*}

Therefore, the correct choice is B.

Find the Derivative of Y with Respect to X y=−cos⁡−1(6x+39)y = - \cos ^ { - 1 } \left( \frac { 6 x + 3 } { 9 } \right)y=−cos−1(96x+3​)

Find the Derivative of Y with Respect to X $y = - \cos ^ { - 1 } \left( \frac { 6 x + 3 } { 9 } \right)$