derivative (x^2-x+1)e^3x

解答

导数

(x^{2} - x + 1) e^{3} x

e^{3} (3 x^{2} - 2 x + 1)

求解步骤

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

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= e^{3} \frac{d}{d x} ((x^{2} - x + 1) x)

使用微分乘法定则:

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

f = x^{2} - x + 1, g = x

= e^{3} (\frac{d}{d x} (x^{2} - x + 1) x + \frac{d x}{d x} (x^{2} - x + 1))

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

\frac{d x}{d x} = 1

= e^{3} ((2 x - 1) x + 1 \cdot (x^{2} - x + 1))

化简

e^{3} ((2 x - 1) x + 1 \cdot (x^{2} - x + 1)) : e^{3} (3 x^{2} - 2 x + 1)

= e^{3} (3 x^{2} - 2 x + 1)

d er i v a t i v e y = 6 x^{2} - 3 x^{3}

d er i v a t i v e y = (5 x - 3) (\frac{4 x - 3}{x})

d er i v a t i v e \frac{- 5}{( 4 x - 2 y + 2 )}

d er i v a t i v e y = 5 x^{8} - 6 x + 12

d er i v a t i v e f (t) = 3 + 8 t - t^{2}