Question

calculati derivata funcției: f(x)= e^2x ×tg (x+2)​

Answer 1

$\it [e^{2x}\cdot tg(x+2)]'=(e^{2x})'\cdot tg(x+2)+e^{2x}[\cdot tg(x+2)]'=\\ \\ \\ = 2e^{2x}\cdot tg(x+2)+e^{2x}\cdot\dfrac{(x+2)'}{sin^2(x+2)}=e^{2x}\Big[2tg(x+2)+\dfrac{1}{sin^2(x+2)}\Big]$

$\it \rule{150}{0.6}$

$\it (e^{2x})'=(2x)'e^{2x}=2e^{2x}\\ \\ (tg x)'=\dfrac{1}{sin^2x}\\ \\ \\ \Big[ tg(x+2)\Big]'=\dfrac{(x+2)'}{sin^2(x+2)}$