What is the derivative of sqrt(x/3) ?

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

What is the first derivative of sqrt(x/3) ?

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

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derivative of

\frac{x}{3}

\frac{1}{2 3 x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 \frac{x}{3}} \cdot \frac{1}{3} : \frac{1}{2 3 x}

= \frac{1}{2 3 x}

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