If y = e^{sqrt{x}},then frac{dy}{dx} equals: | vedclass

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Question

(A) Given the function $y = e^{\sqrt{x}}$.To find the derivative $\frac{dy}{dx}$,we apply the chain rule.Let $u = \sqrt{x} = x^{1/2}$. Then $y = e^u$.

Vedclass · Accepted Answer

$\frac{e^{\sqrt{x}}}{2\sqrt{x}}$

Vedclass · Answer

(A) Given the function $y = e^{\sqrt{x}}$.To find the derivative $\frac{dy}{dx}$,we apply the chain rule.Let $u = \sqrt{x} = x^{1/2}$. Then $y = e^u$.Using the chain rule: $\frac{dy}{dx} = \frac{dy}{du} 	imes \frac{du}{dx}$.$\frac{dy}{du} = \frac{d}{du}(e^u) = e^u = e^{\sqrt{x}}$.$\frac{du}{dx} = \frac{d}{dx}(x^{1/2}) = \frac{1}{2}x^{-1/2} = \frac{1}{2\sqrt{x}}$.Therefore,$\frac{dy}{dx} = e^{\sqrt{x}} 	imes \frac{1}{2\sqrt{x}} = \frac{e^{\sqrt{x}}}{2\sqrt{x}}$.

If $y = e^{\sqrt{x}}$,then $\frac{dy}{dx}$ equals:

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