What is (\partial)/(\partial y)(arctan(9x-9y)) ?

The answer to (\partial)/(\partial y)(arctan(9x-9y)) is -9/((9x-9y)^2+1)

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(\partial)/(\partial y)(arctan(9x-9y))

\frac{\partial}{\partial y} (arctan (9 x - 9 y))

- \frac{9}{( 9 x - 9 y ) ^{2} + 1}

Solution steps

\frac{\partial}{\partial y} (arctan (9 x - 9 y))

Treat

x

as a constant

Apply the chain rule:

\frac{1}{( 9 x - 9 y ) ^{2} + 1} \frac{\partial}{\partial y} (9 x - 9 y)

= \frac{1}{( 9 x - 9 y ) ^{2} + 1} \frac{\partial}{\partial y} (9 x - 9 y)

\frac{\partial}{\partial y} (9 x - 9 y) = - 9

= \frac{1}{( 9 x - 9 y ) ^{2} + 1} (- 9)

Simplify

\frac{1}{( 9 x - 9 y ) ^{2} + 1} (- 9) : - \frac{9}{( 9 x - 9 y ) ^{2} + 1}

= - \frac{9}{( 9 x - 9 y ) ^{2} + 1}

\int sin (x) cos (3 x) d x

x \to 1 lim (x^{(\frac{1}{x - 1})})

x \to x lim (\frac{1}{x})

x \to 0 - lim (\frac{3 x - 1}{2 x})

\int \frac{x}{a x ^{2} + b} d x

What is (\partial)/(\partial y)(arctan(9x-9y)) ?
The answer to (\partial)/(\partial y)(arctan(9x-9y)) is -9/((9x-9y)^2+1)