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Popular >

derivative of arctan(x/b)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x}{b}) = \frac{1}{b}

= \frac{1}{( \frac{x}{b} ) ^{2} + 1} \cdot \frac{1}{b}

Simplify

\frac{1}{( \frac{x}{b} ) ^{2} + 1} \cdot \frac{1}{b} : \frac{b}{x ^{2} + b ^{2}}

= \frac{b}{x ^{2} + b ^{2}}

Popular Examples

integral of sec^2(x/2)

\int sec^{2} (\frac{x}{2}) d x

tangent of f(x)=-2x^3,\at x=-1 tangent of

f (x) = - 2 x^{3}, at x = - 1

slope of (1,-1/2),(-2,-7/2)slope

(1, - \frac{1}{2}), (- 2, - \frac{7}{2})

integral from 0 to pi/2 of x^3cos(2x)

\int_{0}^{\frac{π}{2}} x^{3} cos (2 x) d x

derivative of ((tan(3x^3+x^2)/(e^x))^3)

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

Frequently Asked Questions (FAQ)

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