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

解答

导数

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

3 x^{2} - 6 x + 6

求解步骤

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

使用微分乘法定则:

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

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

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

\frac{d}{d x} (x - 3) = 1

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

= 1 \cdot (x^{2} + 6) + 2 x (x - 3)

化简

1 \cdot (x^{2} + 6) + 2 x (x - 3) : 3 x^{2} - 6 x + 6

= 3 x^{2} - 6 x + 6

\frac{\partial}{\partial x} (8 x cos (x) cos (y))

x \to 1 lim (\frac{∣ x ∣}{x})

x \to 0 lim (h (\frac{1}{x}))

\int 5 x^{3} e^{x^{4}} d x

\frac{d}{d t} (\frac{5}{5 - t})