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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{9 x ^{2} - 4}{x} d x

\int (2 x + 3)^{- 2} d x

y^{^{'}} + 3 y x^{5} = 0

\frac{d}{d x} (w (\frac{x}{50} - F (w, x)))

e^{x}, x^{2} - 1, - 1, 1

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