What is (\partial)/(\partial x)(2yarctan(x)) ?

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

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(\partial)/(\partial x)(2yarctan(x))

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the common derivative:

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

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

Simplify

2 y \frac{1}{x ^{2} + 1} : \frac{2 y}{x ^{2} + 1}

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

y^{^{''}} + 10 y^{^{'}} + 61 y = 0

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

x \to 4 - lim (\frac{3}{x - 2})

\int (x + \frac{1}{5 x}) d x

y = \frac{1}{12 x ^{2}}, y = x, y = \frac{x}{18}

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