Given $y=xe^{2x}$, prove by mathematical induction that \(\displaystyle\frac{\mathrm d^n y}{\mathr

Question

Given $y=xe^{2x}$, prove by mathematical induction that $\displaystyle\frac{\mathrm d^n y}{\mathrm d x^n}=2^{n-1}(2x+n)e^{2x}$ for every $n\in\mathbb Z^+$.

Accepted Answer

$\displaystyle\frac{\mathrm d^n y}{\mathrm d x^n}=2^{n-1}(2x+n)e^{2x}$ for every $n\in\mathbb Z^+$.

Repeated Differentiation of an Exponential Product

Repeated Differentiation of an Exponential Product

Solution:

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