Find the Derivative of the Function $y=8 \cos ^{-1}\left(\sin ^{-1} t\right)$

Find the derivative of the function. $y=8 \cos ^{-1}\left(\sin ^{-1} t\right)$

A) $y^{\prime}=-\frac{8}{\sqrt{1-\left(\sin ^{-1}(t) \right) ^{2}}}$
B) $y^{\prime}=-\frac{8}{\sqrt{\left(1-t^{2}\right) \left(1-\sin ^{-1}(t) \right) }}$
C) $y^{\prime}=-\frac{8}{\sqrt{\left(1+t^{2}\right) \left(1+\left(\sin ^{-1}(t) \right) ^{2}\right) }}$
D) $y^{\prime}=-\frac{8}{\sqrt{\left(1-t^{2}\right) \left(1-\left(\sin ^{-1}(t) \right) ^{2}\right) }}$
E) $y^{\prime}=-\frac{8}{\sqrt{\left(1-t^{2}\right) }}$

Correct Answer:

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