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Popular >

derivative of sqrt(5x-\sqrt{x)}

Solution

\frac{d}{d x} (5 x - x)

Solution

\frac{10 x - 1}{4 x 5 x - x}

Solution steps

\frac{d}{d x} (5 x - x)

Apply the chain rule:

\frac{1}{2 5 x - x} \frac{d}{d x} (5 x - x)

= \frac{1}{2 5 x - x} \frac{d}{d x} (5 x - x)

\frac{d}{d x} (5 x - x) = 5 - \frac{1}{2 x}

= \frac{1}{2 5 x - x} (5 - \frac{1}{2 x})

Simplify

\frac{1}{2 5 x - x} (5 - \frac{1}{2 x}) : \frac{10 x - 1}{4 x 5 x - x}

= \frac{10 x - 1}{4 x 5 x - x}

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt(5x-\sqrt{x)} ?
The derivative of sqrt(5x-\sqrt{x)} is (10sqrt(x)-1)/(4sqrt(x)\sqrt{5x-\sqrt{x)}}
What is the first derivative of sqrt(5x-\sqrt{x)} ?
The first derivative of sqrt(5x-\sqrt{x)} is (10sqrt(x)-1)/(4sqrt(x)\sqrt{5x-\sqrt{x)}}