Question

Use the product rule to differentiate xe^×sinx​

Answer 1

By the product rule,

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