What is the d/(dy)(arctan(x+2y)) ?

The d/(dy)(arctan(x+2y)) is 2/((x+2y)^2+1)

What is the first d/(dy)(arctan(x+2y)) ?

The first d/(dy)(arctan(x+2y)) is 2/((x+2y)^2+1)

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\frac{d}{d y} (arctan (x + 2 y))

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

Solution steps

\frac{d}{d y} (arctan (x + 2 y))

Treat

x

as a constant

Apply the chain rule:

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

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

\frac{d}{d y} (x + 2 y) = 2

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

Simplify

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

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

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\frac{d}{d x} (x - 2)

\int \frac{1}{7 x + 5} d x

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

\int \frac{e ^{2 x}}{( 1 + e ^{2 x} ) ^{3}} d x

What is the d/(dy)(arctan(x+2y)) ?
The d/(dy)(arctan(x+2y)) is 2/((x+2y)^2+1)
What is the first d/(dy)(arctan(x+2y)) ?
The first d/(dy)(arctan(x+2y)) is 2/((x+2y)^2+1)