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Popular >

derivative of arctan(c/x)

Solution

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

Solution

- \frac{c}{c ^{2} + x ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{c}{c ^{2} + x ^{2}}

Popular Examples

tangent of f(x)=(5x)/(x-2),\at x=3 tangent of

f (x) = \frac{5 x}{x - 2}, at x = 3

derivative of 16e^{-2x}

\frac{d}{d x} (16 e^{- 2 x})

sum from n=3 to infinity of 3/2*1/(4^n)

n = 3 \sum \infty \frac{3}{2} \cdot \frac{1}{4 ^{n}}

integral from 0 to 8 of f(x)

\int_{0}^{8} f (x) d x

(dx)/(dt)=(2t^2+x^2)/(tx)

\frac{d x}{d t} = \frac{2 t ^{2} + x ^{2}}{t x}

Frequently Asked Questions (FAQ)

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