What is (\partial)/(\partial x)(arctan(x/3)) ?

The answer to (\partial)/(\partial x)(arctan(x/3)) is 3/(x^2+9)

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(\partial)/(\partial x)(arctan(x/3))

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (\frac{x}{3}) = \frac{1}{3}

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

Simplify

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

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

x \to - 3 + lim (\frac{x}{x ^{2} - 9})

x \to 2 lim (\frac{x ^{3} - 8}{2 x})

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

x \to 3 lim (cos (\frac{1}{x - 3}))

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

What is (\partial)/(\partial x)(arctan(x/3)) ?
The answer to (\partial)/(\partial x)(arctan(x/3)) is 3/(x^2+9)