derivative (x-1)^2e^x

解答

导数

(x - 1)^{2} e^{x}

e^{x} x^{2} - e^{x}

求解步骤

\frac{d}{d x} ((x - 1)^{2} e^{x})

使用微分乘法定则:

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

f = (x - 1)^{2}, g = e^{x}

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

\frac{d}{d x} ((x - 1)^{2}) = 2 (x - 1)

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

= 2 (x - 1) e^{x} + e^{x} (x - 1)^{2}

化简

2 (x - 1) e^{x} + e^{x} (x - 1)^{2} : e^{x} x^{2} - e^{x}

= e^{x} x^{2} - e^{x}

\frac{d}{d x} ((2 x - 1)^{2} ln (2 x - 1))

d er i v a t i v e f (x) = (x) (3 x - 2)

\frac{d y}{d t} = 3 y + y^{6}, y (0) = 1

l a pl a ce t r an s f or m sin (t - 2 π)

\frac{d y}{d x} (x^{2} + 4) = x y