What is (\partial)/(\partial x)(arctan(x-2y)) ?

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

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(\partial)/(\partial x)(arctan(x-2y))

\frac{\partial}{\partial x} (arctan (x - 2 y))

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

Solution steps

\frac{\partial}{\partial x} (arctan (x - 2 y))

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

\int x - x d x

\frac{2}{x}

y^{^{''}} - a y = 0

\int_{1}^{2} x e^{- x^{2}} d x

(0, 0), (- 5, 3)

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