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**satis** Could someone assist with this, please? The task is to differentiate the following equation

$\displaystyle y=xe^{-kx}$

by the chain rule, differentiation should be $\displaystyle e^{f(x)}*f'(x)$ for e, so to me that means

$\displaystyle y'=xe^{-kx}(-k)$ or $\displaystyle y'=-kxe^{-kx}$

unfortunately, my book would disagree with me. According to it, the answer before simplification is

$\displaystyle y'=xe^{-kx}(-k) + e^{-kx}*1$

Can someone please explain to me where the plus and everything after it came from?