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Popular >

derivative of arctan(5/x)

Solution

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

Solution

- \frac{5}{25 + x ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{( \frac{5}{x} ) ^{2} + 1} (- \frac{5}{x ^{2}}) : - \frac{5}{25 + x ^{2}}

= - \frac{5}{25 + x ^{2}}

Popular Examples

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

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

(\partial)/(\partial z)(xze^{yz})

\frac{\partial}{\partial z} (x z e^{yz})

y^'=0.23y-0.0005y^2

y^{^{'}} = 0.23 y - 0.0005 y^{2}

integral from 0 to 60 of (60-y)^2

\int_{0}^{60} (60 - y)^{2} d y

xy^'+y=3xsqrt(y)

x y^{^{'}} + y = 3 x y

Frequently Asked Questions (FAQ)

What is the derivative of arctan(5/x) ?
The derivative of arctan(5/x) is -5/(25+x^2)
What is the first derivative of arctan(5/x) ?
The first derivative of arctan(5/x) is -5/(25+x^2)