Question

Ayuuuiidaa!! Por favor , ¿Como se resuelven estos 3 problemas de derivadas?

Answer 1

Te dejo la 22 y 24, la 23 es muy parecida a la 22.

22
$\begin{matrix} y' & = & \frac{d}{dx} \left(2 x ^ 2 \sqrt{2 + x}\right) \\\\ & = & \sqrt{2 + x} \cdot{} \frac{d}{dx} (2 x ^ 2) + 2 x ^ 2 \cdot{} \frac{d}{dx} (\sqrt{2 + x}) \\\\ & = & 4 x \sqrt{2 + x} + \dfrac{x ^ 2}{\sqrt{2 + x}} \\\\ & = & \dfrac{x}{\sqrt{2 + x}}\left(5x + 8\right) \end{matrix}$


24
$\begin{matrix} y' & = & \frac{d}{dx}\left[(2 x - 5) ^ 2 (x ^ 2 + 1)\right] \\\\ & = & (x ^ 2 + 1)(\frac{d}{dx}[(2x - 5) ^ 2]) + (2 x - 5) ^ 2(\frac{d}{dx}[x ^ 2 + 1]) \\\\ & = & [2(x ^ 2 + 1)(2 x - 5)(\frac{d}{dx}[2 x - 5])] + [2 x (2 x - 5) ^ 2] \\\\ & = & 4(x ^ 2 + 1)(2 x - 5) + 2 x (2 x - 5) ^ 2 \\\\ & = & 2(2 x - 5)(4x ^ 2 - 5x + 2) \end{matrix}$