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

The derivative of sqrt(5/x) is -(sqrt(5))/(2x^{3/2)}

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

The first derivative of sqrt(5/x) is -(sqrt(5))/(2x^{3/2)}

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

- \frac{5}{2 x ^{\frac{3}{2}}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 \frac{5}{x}} (- \frac{5}{x ^{2}}) : - \frac{5}{2 x ^{\frac{3}{2}}}

= - \frac{5}{2 x ^{\frac{3}{2}}}

What is the derivative of sqrt(5/x) ?
The derivative of sqrt(5/x) is -(sqrt(5))/(2x^{3/2)}
What is the first derivative of sqrt(5/x) ?
The first derivative of sqrt(5/x) is -(sqrt(5))/(2x^{3/2)}