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)

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derivative of

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

\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}

\int \frac{x}{x ^{4} - 3 x ^{2} + 2} d x

(sin (\frac{1}{x}))^{^{'}}

f (x) = ln (19 x^{3} + sin (3 x^{2}))

\frac{d}{d X} (X^{3} - 3 X)

x y^{^{'}} + y = - 8 x y^{2}, y (1) = 3

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)