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Popular >

derivative of sqrt(e^{\sqrt{x)}}

Solution

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

Solution

\frac{e ^{x}}{4 x e ^{x}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 e ^{x}} \cdot \frac{e ^{x}}{2 x} : \frac{e ^{x}}{4 x e ^{x}}

= \frac{e ^{x}}{4 x e ^{x}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt(e^{\sqrt{x)}} ?
The derivative of sqrt(e^{\sqrt{x)}} is (e^{sqrt(x)})/(4sqrt(x)\sqrt{e^{\sqrt{x)}}}
What is the first derivative of sqrt(e^{\sqrt{x)}} ?
The first derivative of sqrt(e^{\sqrt{x)}} is (e^{sqrt(x)})/(4sqrt(x)\sqrt{e^{\sqrt{x)}}}