# How do you find the derivative of # y=e^(x^(1/2))#?

A substitution here would help tremendously!

now,

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To find the derivative of ( y = e^{x^{1/2}} ), use the chain rule:

( \frac{dy}{dx} = \frac{d}{dx}(e^{x^{1/2}}) = e^{x^{1/2}} \cdot \frac{d}{dx}(x^{1/2}) )

Apply the power rule to ( x^{1/2} ):

( \frac{dy}{dx} = e^{x^{1/2}} \cdot \frac{1}{2}x^{-1/2} )

So, the derivative is:

( \frac{dy}{dx} = \frac{e^{x^{1/2}}}{2\sqrt{x}} )

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