<s>[INST] 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 $2x\sqrt{2x+5} + x^2  \dfrac{2}{2\sqrt{2x+5}}$
 [/INST] I would use the product rule, which you seem to have tried from your comment above. Here would be the idea:
$\begin{split}
\frac{d[x^2 \sqrt{2x+5} - 6]}{dx}
 &= \frac{dx^2}{dx} \sqrt{2x+5} +  x^2 \frac{d(2x+5)^{\1/2}}{dx} \\
 &= 2x \sqrt{2x+5} + x^2 \frac{1}{2} (2x+5)^{-1/2} \cdot 2 \\
 &= 2x \sqrt{2x+5} + \frac{x^2}{\sqrt{2x+5}}
\end{split}
$
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