derivative of (3x^2-4xe^x)

解答

\frac{d}{d x} ((3 x^{2} - 4 x) e^{x})

3 e^{x} x^{2} + 2 e^{x} x - 4 e^{x}

求解步骤

\frac{d}{d x} ((3 x^{2} - 4 x) e^{x})

使用微分乘法定则:

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

f = 3 x^{2} - 4 x, g = e^{x}

= \frac{d}{d x} (3 x^{2} - 4 x) e^{x} + \frac{d}{d x} (e^{x}) (3 x^{2} - 4 x)

\frac{d}{d x} (3 x^{2} - 4 x) = 6 x - 4

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

= (6 x - 4) e^{x} + e^{x} (3 x^{2} - 4 x)

化简

(6 x - 4) e^{x} + e^{x} (3 x^{2} - 4 x) : 3 e^{x} x^{2} + 2 e^{x} x - 4 e^{x}

= 3 e^{x} x^{2} + 2 e^{x} x - 4 e^{x}

\int \frac{4 x ^{3} - 7 x - 12}{x ^{3} - x ^{2} - 6 x} d x

\frac{d}{d x} (\frac{7}{2 x})

x \to - 1 lim (4 x^{3} + x^{2} + 2 x + 1)

\frac{d y}{d x} = y x^{9} sin (x^{10})

\frac{d}{d x} (\frac{1}{7 x})