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

解答

导数

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

5 x^{4} + 6 x^{2} + 12 x

求解步骤

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

使用微分乘法定则:

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

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

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

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

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

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

化简

2 x (x^{3} + 6) + 3 x^{2} (x^{2} + 2) : 5 x^{4} + 6 x^{2} + 12 x

= 5 x^{4} + 6 x^{2} + 12 x

\int cos (x) e^{- s x} d x

\frac{\partial}{\partial x} (x^{2} + 1 + z^{3})

s l o p e (\frac{5}{8}, - 2), (- \frac{1}{4}, - \frac{1}{4})

t an g e n t y^{2} - x y - 10 = 0, (- 3, - 5)

y^{^{''}} + 6 y = - 294 x^{2} e^{6 x}