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Popular Calculus >

derivative of x^2arctan(x)

Solution

\frac{d}{d x} (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

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x \to 0 lim (\frac{1}{3})

4xy^'-(1+x)y=2xy^2

4 x y^{^{'}} - (1 + x) y = 2 x y^{2}

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factor t^3-6t^2+9t

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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)