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Popular >

derivative of x^2arctan(x)

Solution

derivative of

x^{2} arctan (x)

Solution

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

Solution steps

\frac{d}{d x} (x^{2} arctan (x))

Apply the Product Rule:

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

f = x^{2}, g = arctan (x)

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

\frac{d}{d x} (x^{2}) = 2 x

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

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

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

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

Graph

Popular Examples

integral of 3sin^3(xco)s^5x

\int 3 sin^{3} (x co) s^{5} x d x

integral of 1/((x^2+4)^3)

\int \frac{1}{( x ^{2} + 4 ) ^{3}} d x

derivative of cos(tan(x)e^{-(x/8)^2})

\frac{d}{d x} (cos (tan (x)) e^{- (\frac{x}{8})^{2}})

integral of (x^3)/(x^8+1)

\int \frac{x ^{3}}{x ^{8} + 1} d x

d/(d{y)}({x}{y}{z}^2)

\frac{d}{d y} (x y z^{2})

Frequently Asked Questions (FAQ)

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