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Popular >

derivative of xarctan(x)

Solution

\frac{d}{d x} (x arctan (x))

Solution

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

Solution steps

\frac{d}{d x} (x arctan (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = arctan (x)

= \frac{d x}{d x} arctan (x) + \frac{d}{d x} (arctan (x)) x

\frac{d x}{d x} = 1

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

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

Simplify

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

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

Popular Examples

2y^{''}-y^'+3y=0

2 y^{^{''}} - y^{^{'}} + 3 y = 0

x^2y^{''}-14xy^'+56y=0

x^{2} y^{^{''}} - 14 x y^{^{'}} + 56 y = 0

(dy)/(dx)=e^y(2x^3-4x)

\frac{d y}{d x} = e^{y} (2 x^{3} - 4 x)

integral of ((x^3+2x^2-4)/(x^2))

\int (\frac{x ^{3} + 2 x ^{2} - 4}{x ^{2}}) d x

integral from 1 to 2 of sqrt(x-1)

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

Frequently Asked Questions (FAQ)

What is the derivative of xarctan(x) ?
The derivative of xarctan(x) is arctan(x)+x/(x^2+1)
What is the first derivative of xarctan(x) ?
The first derivative of xarctan(x) is arctan(x)+x/(x^2+1)