What is the derivative of arctan(xy) ?

The derivative of arctan(xy) is y/(x^2y^2+1)

What is the first derivative of arctan(xy) ?

The first derivative of arctan(xy) is y/(x^2y^2+1)

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derivative of

arctan (x y)

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{d}{d 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{d}{d x} (x^{3} + 7)

\int \frac{144 - x ^{2}}{x} d x

\frac{d}{d x} (3 x^{2} - 6 x + 9)

\frac{\partial}{\partial x} (y - \frac{216}{x ^{2}})

tan (x)

What is the derivative of arctan(xy) ?
The derivative of arctan(xy) is y/(x^2y^2+1)
What is the first derivative of arctan(xy) ?
The first derivative of arctan(xy) is y/(x^2y^2+1)