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Popular >

derivative of f(x)=arctan(x/2)

Solution

derivative of

f (x) = arctan (\frac{x}{2})

Solution

\frac{2}{x ^{2} + 4}

Solution steps

\frac{d}{d x} (arctan (\frac{x}{2}))

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x}{2}) = \frac{1}{2}

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

Simplify

\frac{1}{( \frac{x}{2} ) ^{2} + 1} \cdot \frac{1}{2} : \frac{2}{x ^{2} + 4}

= \frac{2}{x ^{2} + 4}

Popular Examples

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y = 4 x - x^{2} (1.3)

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\int \frac{1}{x ^{2} 36 - x ^{2}} d x

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\int_{- π}^{π} sin (x) cos (x) d x

y^'=x^2+x,y(1)=3

y^{^{'}} = x^{2} + x, y (1) = 3

integral of sin^3(6x)cos^2(6x)

\int sin^{3} (6 x) cos^{2} (6 x) d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=arctan(x/2) ?
The derivative of f(x)=arctan(x/2) is 2/(x^2+4)
What is the first derivative of f(x)=arctan(x/2) ?
The first derivative of f(x)=arctan(x/2) is 2/(x^2+4)