Question

Differentiate $e^x(x^3+\sqrt{x})$.

Answer 1

$\frac{d}{dx}[e^x.(x^3+\sqrt{x}\left)\right]=e^x.\frac{d}{dx}(x^3+\sqrt{x})+(x^3+\sqrt{x}).\frac{d}{dx}\left(e^x\right).$

=$e^x\{3x^2+\frac{1}{2}{x}^{-1/2}\}+(x^3+\sqrt{x}).e^x$

=$e^x\{x^3+3x^2+\frac{1}{2\sqrt{x}}+\sqrt{x}\}.$