derivative of (2e^x+x^2ln(x))

解答

\frac{d}{d x} ((2 e^{x} + x^{2}) ln (x))

ln (x) (2 e^{x} + 2 x) + \frac{2 e ^{x} + x ^{2}}{x}

求解步骤

\frac{d}{d x} ((2 e^{x} + x^{2}) ln (x))

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 2 e^{x} + x^{2}, g = ln (x)

= \frac{d}{d x} (2 e^{x} + x^{2}) ln (x) + \frac{d}{d x} (ln (x)) (2 e^{x} + x^{2})

\frac{d}{d x} (2 e^{x} + x^{2}) = 2 e^{x} + 2 x

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= (2 e^{x} + 2 x) ln (x) + \frac{1}{x} (2 e^{x} + x^{2})

\frac{1}{x} (2 e^{x} + x^{2}) = \frac{2 e ^{x} + x ^{2}}{x}

= ln (x) (2 e^{x} + 2 x) + \frac{2 e ^{x} + x ^{2}}{x}

x \to 1 lim (x)

in v erse l a pl a ce \frac{1}{s ^{2}} - \frac{1}{s} + \frac{1}{( s - 2 )}

\int \frac{x ^{2} + 2 x}{x ^{2} + 2 x + 1} d x

\frac{d}{d x} (x - \frac{3}{x})

\frac{d}{d x} (ln (x + x^{2} - 4))