What is the derivative of sqrt(x)(2x+4) ?

The derivative of sqrt(x)(2x+4) is (3x+2)/(sqrt(x))

What is the first derivative of sqrt(x)(2x+4) ?

The first derivative of sqrt(x)(2x+4) is (3x+2)/(sqrt(x))

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\frac{d}{d x} (x (2 x + 4))

\frac{3 x + 2}{x}

Solution steps

\frac{d}{d x} (x (2 x + 4))

Apply the Product Rule:

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

f = x, g = 2 x + 4

= \frac{d}{d x} (x) (2 x + 4) + \frac{d}{d x} (2 x + 4) x

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

\frac{d}{d x} (2 x + 4) = 2

= \frac{1}{2 x} (2 x + 4) + 2 x

Simplify

\frac{1}{2 x} (2 x + 4) + 2 x : \frac{3 x + 2}{x}

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

x \to 7 lim (\frac{x + 6}{x + 1})

(x^{3} + 2 x)^{3}, at x = 4

\int_{0}^{2} x^{6} d x

\int x cos (4 π) x^{2} d x

\frac{d}{d x} (\frac{x ^{2} + x + 2}{2 x})

What is the derivative of sqrt(x)(2x+4) ?
The derivative of sqrt(x)(2x+4) is (3x+2)/(sqrt(x))
What is the first derivative of sqrt(x)(2x+4) ?
The first derivative of sqrt(x)(2x+4) is (3x+2)/(sqrt(x))