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} (x (x - 6)^{2})

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n = 3 \sum \infty \frac{2}{n ^{2} - 1}

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

\int \frac{4}{cos ^{2} ( 2 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)