What is the derivative of sqrt(x/5) ?

The derivative of sqrt(x/5) is 1/(2sqrt(5)\sqrt{x)}

What is the first derivative of sqrt(x/5) ?

The first derivative of sqrt(x/5) is 1/(2sqrt(5)\sqrt{x)}

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

\frac{1}{2 5 x}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{2 \frac{x}{5}} \cdot \frac{1}{5}

Simplify

\frac{1}{2 \frac{x}{5}} \cdot \frac{1}{5} : \frac{1}{2 5 x}

= \frac{1}{2 5 x}

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What is the derivative of sqrt(x/5) ?
The derivative of sqrt(x/5) is 1/(2sqrt(5)\sqrt{x)}
What is the first derivative of sqrt(x/5) ?
The first derivative of sqrt(x/5) is 1/(2sqrt(5)\sqrt{x)}