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Popular >

derivative of sqrt(2+\sqrt{x)}

Solution

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

Solution

\frac{1}{4 x 2 + x}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{2 2 + x} \cdot \frac{1}{2 x}

Simplify

\frac{1}{2 2 + x} \cdot \frac{1}{2 x} : \frac{1}{4 x 2 + x}

= \frac{1}{4 x 2 + x}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt(2+\sqrt{x)} ?
The derivative of sqrt(2+\sqrt{x)} is 1/(4sqrt(x)\sqrt{2+\sqrt{x)}}
What is the first derivative of sqrt(2+\sqrt{x)} ?
The first derivative of sqrt(2+\sqrt{x)} is 1/(4sqrt(x)\sqrt{2+\sqrt{x)}}