Mathematicsddx(x+1)(3x)=

$\frac{d}{d x} (\sqrt{x} + 1) (3 \sqrt{x}) =$

A
$3 (1 + \frac{1}{2 \sqrt{x}})$
B
$3 (1 - \frac{1}{2 \sqrt{x}})$
C
$3 (1 + \frac{1}{\sqrt{x}})$
D
$3 (1 - \frac{1}{\sqrt{x}})$

Solution:

$\frac{d}{d x} [3 x + 3 \sqrt{x}]$

$= 3 + 3 \cdot \frac{d}{d x} x^{\frac{1}{2}}$

$= 3 + 3 \cdot \frac{1}{2} \cdot x^{\frac{1}{2} - 1}$

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

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