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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

x(dy)/(dx)=y+sqrt(x^2+y^2)

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

integral of sin^3(x)x

\int sin^{3} (x) x d x

limit as x approaches 1 of sqrt(1+x)

x \to 1 lim (1 + x)

(d^2)/(dx^2)(8{z}(x)(x)^2e^{{z}(x)})

\frac{d ^{2}}{d x ^{2}} (8 z (x) (x)^{2} e^{z (x)})

derivative of f(x)=sqrt(2x+9)derivative of

f (x) = 2 x + 9

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)