What is (\partial)/(\partial y)(arctan(x-y)) ?

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

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(\partial)/(\partial y)(arctan(x-y))

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (x - y) = - 1

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

Simplify

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

x \to \infty + lim (0)

\int sec^{2} (2 x + 1) d x

\frac{\partial}{\partial x} (2 x - 5)

\frac{\partial}{\partial x} (\frac{u - v}{u + v})

\int 6 x arccos (6 x) d x

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