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Popular >

derivative of xarctan(sqrt(x))

Solution

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

Popular Examples

integral of x^{7/3}

\int x^{\frac{7}{3}} d x

(\partial)/(\partial z)(x+2y+z)

\frac{\partial}{\partial z} (x + 2 y + z)

integral from 0 to 4 of sqrt(1+e^{-2y)}

\int_{0}^{4} 1 + e^{- 2 y} d y

integral of (28s+28)/((s^2+1)(s-1)^3)

\int \frac{28 s + 28}{( s ^{2} + 1 ) ( s - 1 ) ^{3}} d s

(\partial)/(\partial x)(3x+4y^2+3x^2y^3)

\frac{\partial}{\partial x} (3 x + 4 y^{2} + 3 x^{2} y^{3})

Frequently Asked Questions (FAQ)

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