What is the derivative of (e^x)^{1/2} ?

The derivative of (e^x)^{1/2} is e^{x/2} 1/2

What is the first derivative of (e^x)^{1/2} ?

The first derivative of (e^x)^{1/2} is e^{x/2} 1/2

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derivative of

(e^{x})^{\frac{1}{2}}

e^{\frac{x}{2}} \frac{1}{2}

Solution steps

\frac{d}{d x} ((e^{x})^{\frac{1}{2}})

Simplify

(e^{x})^{\frac{1}{2}} : e^{\frac{x}{2}}

= \frac{d}{d x} (e^{\frac{x}{2}})

Apply the chain rule:

e^{\frac{x}{2}} \frac{d}{d x} (\frac{x}{2})

= e^{\frac{x}{2}} \frac{d}{d x} (\frac{x}{2})

\frac{d}{d x} (\frac{x}{2}) = \frac{1}{2}

= e^{\frac{x}{2}} \frac{1}{2}

cot^{4} (x)

y = 6 x^{- 2}

\frac{1}{( z - 1 )}

y = 25

sin^{35} (x)

What is the derivative of (e^x)^{1/2} ?
The derivative of (e^x)^{1/2} is e^{x/2} 1/2
What is the first derivative of (e^x)^{1/2} ?
The first derivative of (e^x)^{1/2} is e^{x/2} 1/2