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Popular >

derivative of arctan(3/x)

Solution

\frac{d}{d x} (arctan (\frac{3}{x}))

Solution

- \frac{3}{9 + x ^{2}}

Solution steps

\frac{d}{d x} (arctan (\frac{3}{x}))

Apply the chain rule:

\frac{1}{( \frac{3}{x} ) ^{2} + 1} \frac{d}{d x} (\frac{3}{x})

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

\frac{d}{d x} (\frac{3}{x}) = - \frac{3}{x ^{2}}

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

Simplify

\frac{1}{( \frac{3}{x} ) ^{2} + 1} (- \frac{3}{x ^{2}}) : - \frac{3}{9 + x ^{2}}

= - \frac{3}{9 + x ^{2}}

Graph

Popular Examples

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\int 2 sin (\frac{x}{3}) d x

limit as x approaches 0-of (cos^2(x))/x

x \to 0 - lim (\frac{cos ^{2} ( x )}{x})

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\int x^{4} 8 + x^{5} d x

derivative of ((x+b)(x-a))/((x-b))derivative of

\frac{( x + b ) ( x - a )}{( x - b )}

derivative of x^3*y

\frac{d}{d x} (x^{3} \cdot y)

Frequently Asked Questions (FAQ)

What is the derivative of arctan(3/x) ?
The derivative of arctan(3/x) is -3/(9+x^2)
What is the first derivative of arctan(3/x) ?
The first derivative of arctan(3/x) is -3/(9+x^2)