Differentiating $x^2 \sqrt{2x+5}-6$ How do I differentiate this function: f(x)= $x^2  \sqrt{2x+5}-6$
I had: I had $2x\sqrt{2x+5} + x^2  \dfrac{1}{2\sqrt{2x+5}}$ but the correction model said it was I had $2x\sqrt{2x+5} + x^2  \dfrac{2}{2\sqrt{2x+5}}$

Work from the outside in. Begin by differentiating it term by term: $$f\,'(x)=\frac{d}{dx}\left(x^2\sqrt{2x+5}\right)-\frac{d}{dx}(6)=\frac{d}{dx}\left(x^2\sqrt{2x+5}\right)-0\;.$$
Now you have to calculate the derivative of $x^2\sqrt{2x+5}$. This is a product, so you use the product rule:
$$\left[x^2\sqrt{2x+5}\right]'=x^2\left[\sqrt{2x+5}\right]'+\left[x^2\right]'\sqrt{2x+5}\;.$$
To complete the differentiation you’ll need the derivative of $x^2$, which is very easy, and the derivative of $\sqrt{2x+5}$. That one is also pretty easy once you rewrite the function as $(2x+5)^{1/2}$: the power rule and the chain rule will take care of it.
