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Popular >

derivative of arctan(a/x)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of 1/(1+sin(x)+cos(x))

\int \frac{1}{1 + sin ( x ) + cos ( x )} d x

f (x) = \frac{1}{3 x + 2}

integral of (9x^2-36x)/4+18

\int \frac{9 x ^{2} - 36 x}{4} + 18 d x

(dy)/(dx)=cos(x+y)

\frac{d y}{d x} = cos (x + y)

(\partial)/(\partial y)(cos(x)-y)

\frac{\partial}{\partial y} (cos (x) - y)

Frequently Asked Questions (FAQ)

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