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Popular >

derivative of (x^2+1arctan(x))

Solution

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

Solution

2 x arctan (x) + 1

Solution steps

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

Apply the Product Rule:

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

f = x^{2} + 1, g = arctan (x)

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

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

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

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

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

= 2 x arctan (x) + 1

Graph

Popular Examples

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

\int \frac{1}{x ^{2}} - \frac{4}{x ^{3}} d x

limit as x approaches 0-of 1/(x^3)

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

limit as x approaches 0-of x^x

x \to 0 - lim (x^{x})

integral of (3x^5-2x^3+3)/(x^2)

\int \frac{3 x ^{5} - 2 x ^{3} + 3}{x ^{2}} d x

derivative of 4^x-7

\frac{d}{d x} (4^{x} - 7)

Frequently Asked Questions (FAQ)

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