What is the derivative of sqrt(pi/(2x)) ?

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

What is the first derivative of sqrt(pi/(2x)) ?

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

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\frac{d}{d x} (\frac{π}{2 x})

- \frac{π}{2 2 x ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{π}{2 x})

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{π}{2 2 x ^{\frac{3}{2}}}

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