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Use the product rule to differentiate xe^×sinx​

1 Answer

5 votes

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)}

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