Differentiate the following with respect to x | vedclass

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(A) Let $y = e^{\sin ^{-1} x}$.Differentiating with respect to $x$,we use the chain rule:$\frac{dy}{dx} = \frac{d}{dx}(e^{\sin ^{-1} x})$$\frac{dy}{dx

Vedclass · Accepted Answer

$\frac{e^{\sin ^{-1} x}}{\sqrt{1-x^{2}}}$

Vedclass · Answer

(A) Let $y = e^{\sin ^{-1} x}$.Differentiating with respect to $x$,we use the chain rule:$\frac{dy}{dx} = \frac{d}{dx}(e^{\sin ^{-1} x})$$\frac{dy}{dx} = e^{\sin ^{-1} x} \cdot \frac{d}{dx}(\sin ^{-1} x)$Since the derivative of $\sin ^{-1} x$ is $\frac{1}{\sqrt{1-x^2}}$,we have:$\frac{dy}{dx} = e^{\sin ^{-1} x} \cdot \frac{1}{\sqrt{1-x^2}}$$\frac{dy}{dx} = \frac{e^{\sin ^{-1} x}}{\sqrt{1-x^2}}$,where $x \in (-1, 1)$.

Differentiate the following with respect to $x$: $e^{\sin ^{-1} x}$

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