Question

Derivada de
$y=e^5^xln(x^2-2)$

Answer 1

$\\ y = e^5^xLn(x^2-2) \\ \\ y' = (e^5^x)'*(5x)'Ln(x^2-2) + e^5^x[Ln(x^2-2)]'*(x^2-2)' \\ \\ y' = e^5^x*5Ln(x^2-2) + e^5^x* \frac{1}{x^2-2} *(2x-0) \\ \\ y' = 5e^5^xLn(x^2-2)+ \frac{2xe^5^x}{x^2-2}$

Answer 2

$\sf \displaystyle y=e^{5x}in\left(x^2-2\right)\\\\\\\frac{d}{dx}\left(e^{5x}in\left(x^2-2\right)\right)\\\\\\=in\frac{d}{dx}\left(e^{5x}\left(x^2-2\right)\right)\\\\\\=in\left(\frac{d}{dx}\left(e^{5x}\right)\left(x^2-2\right)+\frac{d}{dx}\left(x^2-2\right)e^{5x}\right)\\\\\\\to \boxed{\sf =in\left(e^{5x}\cdot \:5\left(x^2-2\right)+2xe^{5x}\right)}$