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Popular >

derivative of e^{x^{1/2}}

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

Popular Examples

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f (x) = 2 x^{3} - 3 x^{2} + 3, at x = 1

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\frac{1}{2 x ^{6}}

derivative of 2-2x

\frac{d}{d x} (2 - 2 x)

integral from 1 to 8 of x^{1/3}

\int_{1}^{8} x^{\frac{1}{3}} d x

integral from 0 to 1 of (15)/(4y-1)

\int_{0}^{1} \frac{15}{4 y - 1} d y

Frequently Asked Questions (FAQ)

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