Find the derivative of y with respect to x.
-$$y = \sin ^ { - 1 } \left( e ^ { 6 t } \right)$$
A) $\frac { 6 e ^ { 6 t } } { \sqrt { 1 - e ^ { 36 t } } }$
B) $\frac { - 6 e ^ { 6 t } } { \sqrt { 1 - e ^ { 12 t } } }$
C) $\frac { 6 e ^ { 6 t } } { \sqrt { 1 - e ^ { 12 t } } }$
D) $\frac { e ^ { 6 t } } { \sqrt { 1 - e ^ { 12 t } } }$

Question

Quizplus · Accepted Answer

We can use the chain rule and the identity $\frac{d}{dx}\sin^{-1}(x)=\frac{1}{\sqrt{1-x^2}}$ to get:
$$\frac{dy}{dx}=\frac{d}{dx}\sin^{-1}(e^{6t})=\frac{1}{\sqrt{1-(e^{6t})^2}}\cdot\frac{d}{dx}(e^{6t})=\frac{6e^{6t}}{\sqrt{1-e^{12t}}}$$
Therefore, the answer is $\boxed{	extbf{(C)}}$.

Find the Derivative of Y with Respect to X y=sin⁡−1(e6t)y = \sin ^ { - 1 } \left( e ^ { 6 t } \right)y=sin−1(e6t)

Find the Derivative of Y with Respect to X $y = \sin ^ { - 1 } \left( e ^ { 6 t } \right)$