What is (\partial)/(\partial y)(arctan(x+8y)) ?

The answer to (\partial)/(\partial y)(arctan(x+8y)) is 8/((x+8y)^2+1)

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(\partial)/(\partial y)(arctan(x+8y))

\frac{\partial}{\partial y} (arctan (x + 8 y))

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

Solution steps

\frac{\partial}{\partial y} (arctan (x + 8 y))

Treat

x

as a constant

Apply the chain rule:

\frac{1}{( x + 8 y ) ^{2} + 1} \frac{\partial}{\partial y} (x + 8 y)

= \frac{1}{( x + 8 y ) ^{2} + 1} \frac{\partial}{\partial y} (x + 8 y)

\frac{\partial}{\partial y} (x + 8 y) = 8

= \frac{1}{( x + 8 y ) ^{2} + 1} \cdot 8

Simplify

\frac{1}{( x + 8 y ) ^{2} + 1} \cdot 8 : \frac{8}{( x + 8 y ) ^{2} + 1}

= \frac{8}{( x + 8 y ) ^{2} + 1}

\frac{d}{d x} (\frac{1 - 3 x}{4 + x})

y = 9 x^{2} e^{x}

n = 1 \sum \infty (- 5)^{- n}

\frac{d}{d x} (sin^{2} (x) + 2^{s i n (x)})

n = 1 \sum \infty \frac{n}{n ^{2} + 1}

What is (\partial)/(\partial y)(arctan(x+8y)) ?
The answer to (\partial)/(\partial y)(arctan(x+8y)) is 8/((x+8y)^2+1)