What is the derivative of sqrt(x)(x+1) ?

The derivative of sqrt(x)(x+1) is (3x+1)/(2sqrt(x))

What is the first derivative of sqrt(x)(x+1) ?

The first derivative of sqrt(x)(x+1) is (3x+1)/(2sqrt(x))

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\frac{d}{d x} (x (x + 1))

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

Solution steps

\frac{d}{d x} (x (x + 1))

Apply the Product Rule:

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

f = x, g = x + 1

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

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

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

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

Simplify

\frac{1}{2 x} (x + 1) + 1 \cdot x : \frac{3 x + 1}{2 x}

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

What is the derivative of sqrt(x)(x+1) ?
The derivative of sqrt(x)(x+1) is (3x+1)/(2sqrt(x))
What is the first derivative of sqrt(x)(x+1) ?
The first derivative of sqrt(x)(x+1) is (3x+1)/(2sqrt(x))