2. Differentiate the following w.r.t. x: 

e ^{\sin ^{-1}x}

Answers (1)

Given function is
f(x)=e ^{\sin ^{-1}x}
Let g(x)={\sin ^{-1}x}
Then,
f(x)=e^{g(x)}
Now, differentiation w.r.t. x
f^{'}(x)=g^{'}(x).e^{g(x)}                   -(i)
g(x) = \sin^{-1}x \Rightarrow g^{'}(x ) = \frac{1}{\sqrt{1-x^2}} 
Put this value in our equation (i)
f^{'}(x) = \frac{1}{\sqrt{1-x^2}}.e^{\sin^{-1}x} = \frac{e^{\sin^{-1}x}}{\sqrt{1-x^2}}

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