Question

Find the derivative by first principle in examples of :
$3x^2+4\left(2\right)x\sqrt{x}$

Answer 1

Given,

$\frac{d}{dx}(3x^2+4\left(2\right)x\sqrt{x})$

$=\frac{d}{dx}\left(3x^2\right)+\frac{d}{dx}(4\cdot 2x\sqrt{x})$

$=6x+8(\frac{d}{dx}\left(x\right)\sqrt{x}+\frac{d}{dx}\left(\sqrt{x}\right)x)$

$=6x+8(1\cdot \sqrt{x}+\frac{1}{2\sqrt{x}}x)$

$=6x+8(1\cdot \sqrt{x}+\frac{\sqrt{x}}{2})$

$=6x+12\sqrt{x}$