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Popular >

derivative of sqrt(9+\sqrt{4x)}

Solution

\frac{d}{d x} (9 + 4 x)

Solution

\frac{1}{2 x 9 + 2 x}

Solution steps

\frac{d}{d x} (9 + 4 x)

Apply the chain rule:

\frac{1}{2 9 + 4 x} \frac{d}{d x} (9 + 4 x)

= \frac{1}{2 9 + 4 x} \frac{d}{d x} (9 + 4 x)

\frac{d}{d x} (9 + 4 x) = \frac{1}{x}

= \frac{1}{2 9 + 4 x} \cdot \frac{1}{x}

Simplify

\frac{1}{2 9 + 4 x} \cdot \frac{1}{x} : \frac{1}{2 x 9 + 2 x}

= \frac{1}{2 x 9 + 2 x}

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt(9+\sqrt{4x)} ?
The derivative of sqrt(9+\sqrt{4x)} is 1/(2sqrt(x)\sqrt{9+2\sqrt{x)}}
What is the first derivative of sqrt(9+\sqrt{4x)} ?
The first derivative of sqrt(9+\sqrt{4x)} is 1/(2sqrt(x)\sqrt{9+2\sqrt{x)}}