What is the derivative of sqrt(3+\sqrt{8x)} ?

The derivative of sqrt(3+\sqrt{8x)} is 1/(sqrt(2)\sqrt{x)sqrt(3+2\sqrt{2)sqrt(x)}}

What is the first derivative of sqrt(3+\sqrt{8x)} ?

The first derivative of sqrt(3+\sqrt{8x)} is 1/(sqrt(2)\sqrt{x)sqrt(3+2\sqrt{2)sqrt(x)}}

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\frac{d}{d x} (3 + 8 x)

\frac{1}{2 x 3 + 2 2 x}

Solution steps

\frac{d}{d x} (3 + 8 x)

Apply the chain rule:

\frac{1}{2 3 + 8 x} \frac{d}{d x} (3 + 8 x)

= \frac{1}{2 3 + 8 x} \frac{d}{d x} (3 + 8 x)

\frac{d}{d x} (3 + 8 x) = \frac{2}{x}

= \frac{1}{2 3 + 8 x} \frac{2}{x}

Simplify

\frac{1}{2 3 + 8 x} \frac{2}{x} : \frac{1}{2 x 3 + 2 2 x}

= \frac{1}{2 x 3 + 2 2 x}

What is the derivative of sqrt(3+\sqrt{8x)} ?
The derivative of sqrt(3+\sqrt{8x)} is 1/(sqrt(2)\sqrt{x)sqrt(3+2\sqrt{2)sqrt(x)}}
What is the first derivative of sqrt(3+\sqrt{8x)} ?
The first derivative of sqrt(3+\sqrt{8x)} is 1/(sqrt(2)\sqrt{x)sqrt(3+2\sqrt{2)sqrt(x)}}