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Popular Calculus >

derivative of sqrt(x/a)

Solution

\frac{d}{d x} (\frac{x}{a})

Solution

\frac{1}{2 a x}

Solution steps

\frac{d}{d x} (\frac{x}{a})

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x}{a}) = \frac{1}{a}

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

Simplify

\frac{1}{2 \frac{x}{a}} \cdot \frac{1}{a} : \frac{1}{2 a x}

= \frac{1}{2 a x}

Graph

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Frequently Asked Questions (FAQ)

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