What is (\partial)/(\partial x)(arctan(x/2)) ?

The answer to (\partial)/(\partial x)(arctan(x/2)) is 2/(x^2+4)

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(\partial)/(\partial x)(arctan(x/2))

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{\partial}{\partial 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}

\frac{d}{d x} (y e^{- 3 x})

x^{2} + x - 3

- t^{3} + 15 t^{2} - 72 t

\frac{\partial}{\partial y} (3 x^{2} + 4 y^{2})

x \to 0 lim (1 + cos^{3} (x))

What is (\partial)/(\partial x)(arctan(x/2)) ?
The answer to (\partial)/(\partial x)(arctan(x/2)) is 2/(x^2+4)