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

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

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

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

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

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

Simplify

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

\frac{d}{d x} (\frac{8 e ^{x}}{2 e ^{x} + 1})

\int_{0}^{\frac{1}{2}} 1 - x^{2} d x

\int (1 - t) cos (t^{2} - 2 t) d t

\frac{d}{d x} (cos (x π))

\int e^{1.25 x} - 4 x d x

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