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受欢迎的代数 >

d/(dt)((x)(-2x(x-8)))

解答

\frac{d}{d t} ((t) (- 2 t (t - 8)))

解答

- 2 (3 t^{2} - 16 t)

求解步骤

\frac{d}{d t} ((t) (- 2 t (t - 8)))

化简

(t) (- 2 t (t - 8)) : - 2 t^{2} (t - 8)

= \frac{d}{d t} (- 2 t^{2} (t - 8))

将常数提出:

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

= - 2 \frac{d}{d t} (t^{2} (t - 8))

使用微分乘法定则:

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

f = t^{2}, g = t - 8

= - 2 (\frac{d}{d t} (t^{2}) (t - 8) + \frac{d}{d t} (t - 8) t^{2})

\frac{d}{d t} (t^{2}) = 2 t

\frac{d}{d t} (t - 8) = 1

= - 2 (2 t (t - 8) + 1 \cdot t^{2})

化简

- 2 (2 t (t - 8) + 1 \cdot t^{2}) : - 2 (3 t^{2} - 16 t)

= - 2 (3 t^{2} - 16 t)

流行的例子

展开 (2(2y+19))/3

e x p an d \frac{2 ( 2 y + 19 )}{3}

展开 (sqrt(50))/2

e x p an d \frac{50}{2}

展开 (7(7b+7))/8

e x p an d \frac{7 ( 7 b + 7 )}{8}

展开 (3-5i)(4+7_{i})

e x p an d (3 - 5 i) (4 + 7_{i})

奇偶性 t(-5,-6)

p a r i t y t (- 5, - 6)