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))

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

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 )}

\int_{36}^{x} 1 + 9 x d x

\frac{t - t}{t ^{\frac{1}{7}}}

\frac{3 x ^{2} + 1}{2 x}

\int cos (x) lo g_{10} (2) 2^{x} d x

\frac{d}{d x} (x sin (y - z))

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))