Question

How do you find the derivative of 2^xlog2(x^2+2x+2)/2

Answer 1

$\bf 2^{\cfrac{}{}log_2\left(\frac{x^2+2x+2}{2} \right)} \\ -----------------------------\\\\ \textit{recall the log cancellation rule of }\qquad {{ a}}^{log_{{ a}}x}=x\\ -----------------------------\\ \\ thus \\\\ 2^{\cfrac{}{}log_2\left(\frac{x^2+2x+2}{2} \right)}\impliedby \textit{base of log and expression are the same, thus} \\\\\\ \implies \cfrac{x^2+2x+2}{2}\implies \cfrac{x^2}{2}+\cfrac{2x}{2}+\cfrac{2}{2}\implies \cfrac{1}{2}x^2+x+1$

and pretty sure you can take the derivative of that