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Popular >

derivative of arctan(pi/x)

Solution

\frac{d}{d x} (arctan (\frac{π}{x}))

Solution

- \frac{π}{π ^{2} + x ^{2}}

Solution steps

\frac{d}{d x} (arctan (\frac{π}{x}))

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{π}{π ^{2} + x ^{2}}

Popular Examples

derivative of 1/(tan(x))derivative of

\frac{1}{tan ( x )}

(\partial)/(\partial y)(5+xln(xy-7))

\frac{\partial}{\partial y} (5 + x ln (x y - 7))

derivative of x^2+1/(x^2)derivative of

x^{2} + \frac{1}{x ^{2}}

derivative of (x+3ln(4x+2))

\frac{d}{d x} ((x + 3) ln (4 x + 2))

simplify (x^2}{100}+8+\frac{20)/x simplify

\frac{x ^{2}}{100} + 8 + \frac{20}{x}

Frequently Asked Questions (FAQ)

What is the derivative of arctan(pi/x) ?
The derivative of arctan(pi/x) is -pi/(pi^2+x^2)
What is the first derivative of arctan(pi/x) ?
The first derivative of arctan(pi/x) is -pi/(pi^2+x^2)