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Popular >

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}

Popular Examples

sum from n=0 to infinity of 1/(3^n+1)

n = 0 \sum \infty \frac{1}{3 ^{n} + 1}

derivative of 1/2 x^4+11x^3+30x^2 derivative of

\frac{1}{2} x^{4} + 11 x^{3} + 30 x^{2}

(2dy)/(dx)+5y=4

\frac{2 d y}{d x} + 5 y = 4

limit as x approaches 0 of 1/3

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

limit as x approaches 0 of f(x)x

x \to 0 lim (f (x) x)

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)