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 \frac{1}{x} ln (x^{2}) d x

x \to 18 lim (\frac{1}{x - 18})

x \to 1 lim (f (x) (5 - x))

x \to 2 lim (5 x^{3} - 3 x + 1)

\frac{d y}{d t} - 2 t y = 6 t^{2} e^{t^{2}}

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