Differentiate the following functions with respect to `e^(sin^{-1}{2x}`

Explanation

On differentiating y with respect to `x`, we get



`frac{d y}{d x}=frac{d}{d x}(e^{sin ^{-1} 2 x}) `


`text { We know } frac{d}{d x}(e^{x})=e^{x} `


`Rightarrow frac{d y}{d x}=e^{sin ^{-1} 2 x} frac{d}{d x}(sin ^{-1} 2 x)`



[using chain rule]


We have


...