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Popular >

derivative of x*arctan(sqrt(x))

Solution

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

Solution

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

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

Simplify

1 \cdot arctan (x) + \frac{1}{2 x ( x + 1 )} x : arctan (x) + \frac{x}{2 ( x + 1 )}

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

Graph

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\int (\frac{1}{2} (1 - cos (2 x)))^{2} d x

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x \to - 0.1 lim (x^{3} + 6 x^{2} + x)

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\frac{d}{d x} (e^{2 x - 1})

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\int \frac{3 x ^{2} - 8 x + 1}{x ^{3} - 4 x ^{2} + x + 6} d x

integral of sin(2x)sin(4x)sin(6x)

\int sin (2 x) sin (4 x) sin (6 x) d x

Frequently Asked Questions (FAQ)

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