# Math Help - determine derivative 2

1. ## determine derivative 2

determine the derivative of $g(x)=\sqrt{x}(2x+3)^2$

2. show some work u can use this

(g.f)' = f'.g + g'.f

3. so

$x^{\frac{1}{2}}(2x+3)^2$

$\frac{1}{2}x^{\frac{-1}{2}}(2x+3)^2+x^{\frac{1}{2}}(4(2x+3))$

is that how?

4. Yes, that's correct.

5. Originally Posted by euclid2
so

$x^{\frac{1}{2}}(2x+3)^2$

$\frac{1}{2}x^{\frac{-1}{2}}(2x+3)^2+x^{\frac{1}{2}}(4(2x+3))$

is that how?
You can clean it up with some factorisation...

$\frac{1}{2}x^{-\frac{1}{2}}(2x + 3)^2 + 4x^{\frac{1}{2}}(2x + 3) = (2x + 3)\left(\frac{2x + 3}{2\sqrt{x}} + 4\sqrt{x}\right)$

$= (2x+3)\left(\frac{2x + 3 + 8x}{2\sqrt{x}}\right)$

$= \frac{(2x+3)(10x+3)}{2\sqrt{x}}$