Question

use the product rule to differentiate xe^×sinx​

Answer 1

By the product rule,

$\dfrac{d(x e^x \sin(x))}{dx} = \dfrac{dx}{dx} e^x \sin(x) + x \dfrac{de^x}{dx} \sin(x) + x e^x \dfrac{d\sin(x)}{dx} \\\\ ~~~~~~~~~~~~~~~~~~ = \boxed{e^x \sin(x) + x e^x \sin(x) + x e^x \cos(x)}$