derivative e^x(3x^2-6x+6)

解答

导数

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

3 e^{x} x^{2}

求解步骤

\frac{d}{d x} (e^{x} (3 x^{2} - 6 x + 6))

使用微分乘法定则:

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

f = e^{x}, g = 3 x^{2} - 6 x + 6

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

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

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

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

化简

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

= 3 e^{x} x^{2}

x \to 0 - lim (7 - 2 x)

\int 3 x^{3} - 5 x^{2} + 3 x + 4 d x

d er i v a t i v e (x + 1)^{x + 1}

f (θ) = e^{θ}

\frac{d}{d x} (cos (e^{4 x}))