Word Count : 236

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Let $y = e^m \sin^{-1}x$. First, we compute derivatives with respect to $x$. Let $u = \sin^{-1}x$, then $y = e^{mu}$. First derivative: $$ y_1 = \frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx} = m e^{mu} \cdot \frac{1}{\sqrt{1-x^2}} = \frac{m e^{m \sin^{-1}x}}{\sqrt{1-x^2}}. $$ Second derivative: $$ y_2 = \frac{d}{dx} \left(\frac{m e^{m u}}{\sqrt{1-x^2}}\right) = m \frac{d}{dx} \left( e^{mu} (1-x^2)^{-1/2} \right). $$ Using ________ ___ ___ _________ ___ ________ _________ _______ __________ ____.
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