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Popular Calculus >

derivative of sqrt(3x+\sqrt{x)}

Solution

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

Solution

\frac{6 x + 1}{4 x 3 x + x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 3 x + x} (3 + \frac{1}{2 x}) : \frac{6 x + 1}{4 x 3 x + x}

= \frac{6 x + 1}{4 x 3 x + x}

Graph

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\int x^{3} sin (5 x) d x

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt(3x+\sqrt{x)} ?
The derivative of sqrt(3x+\sqrt{x)} is (6sqrt(x)+1)/(4sqrt(x)\sqrt{3x+\sqrt{x)}}
What is the first derivative of sqrt(3x+\sqrt{x)} ?
The first derivative of sqrt(3x+\sqrt{x)} is (6sqrt(x)+1)/(4sqrt(x)\sqrt{3x+\sqrt{x)}}