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Popular >

derivative of x*arctan(x)

Solution

\frac{d}{d x} (x \cdot 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}

Graph

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(\partial)/(\partial y)(y+6xy^2)

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\int 16 x^{3} d x

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f (x) = \frac{2}{x}

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n = 0 \sum \infty \frac{4}{7 ^{n}}

Frequently Asked Questions (FAQ)

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