derivative of (7x^2-14x+14e^x)

解答

\frac{d}{d x} ((7 x^{2} - 14 x + 14) e^{x})

7 e^{x} x^{2}

求解步骤

\frac{d}{d x} ((7 x^{2} - 14 x + 14) e^{x})

使用微分乘法定则:

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

f = 7 x^{2} - 14 x + 14, g = e^{x}

= \frac{d}{d x} (7 x^{2} - 14 x + 14) e^{x} + \frac{d}{d x} (e^{x}) (7 x^{2} - 14 x + 14)

\frac{d}{d x} (7 x^{2} - 14 x + 14) = 14 x - 14

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

= (14 x - 14) e^{x} + e^{x} (7 x^{2} - 14 x + 14)

化简

(14 x - 14) e^{x} + e^{x} (7 x^{2} - 14 x + 14) : 7 e^{x} x^{2}

= 7 e^{x} x^{2}

\int \frac{1}{( x - 1 ) ( x - 2 ) ( x - 3 )} d x

\frac{d}{d x} (- \frac{30}{x ^{4}})

\int (1 - 2 x^{2} + 3 x^{3}) d x

l a pl a ce t r an s f or m e^{- t} \cdot sin (2 t)

f (x) = - sin (2 x) \cdot 2