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

The answer to (\partial)/(\partial x)(arctan(xy)) is y/(x^2y^2+1)

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(\partial)/(\partial x)(arctan(xy))

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

\frac{y}{x ^{2} y ^{2} + 1}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x y) = y

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

Simplify

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

= \frac{y}{x ^{2} y ^{2} + 1}

\frac{\partial}{\partial x} (5 z^{3} cot (x z))

f (x) = 15 3 x

8 sin^{3} (x)

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

\frac{d}{d x} (e^{x s e c (x)})

What is (\partial)/(\partial x)(arctan(xy)) ?
The answer to (\partial)/(\partial x)(arctan(xy)) is y/(x^2y^2+1)