Question

derivação y=e^2x.cosx

Answer 1

Seja $f(x)=e^{2x}\cos x$.

Assim,

$\displaystyle \frac{\mathrm{df}}{\mathrm{d}x}=\frac{\mathrm{d}}{\mathrm{d}x}e^{2x}\cos x \\\\ = (e^{2x})'\cos x+e^{2x}(\cos x)' \\\\ = \left((2x)'e^{2x} \right )\cos x+e^{2x} \left (-(x)'\sin x \right ) \\\\ = (2e^{2x})\cos x+e^{2x}(-\sin x) \\\\ = 2e^{2x}\cos x-e^{2x}\sin x \\\\ = e^{2x}(2\cos x-\sin x).$

Bons estudos, ma dear.