derivative-2t(6t^6-1)^6

解答

导数

- 2 t (6 t^{6} - 1)^{6}

- 2 ((6 t^{6} - 1)^{6} + 216 t^{6} (6 t^{6} - 1)^{5})

求解步骤

\frac{d}{d t} (- 2 t (6 t^{6} - 1)^{6})

将常数提出:

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

= - 2 \frac{d}{d t} (t (6 t^{6} - 1)^{6})

使用微分乘法定则:

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

f = t, g = (6 t^{6} - 1)^{6}

= - 2 (\frac{d t}{d t} (6 t^{6} - 1)^{6} + \frac{d}{d t} ((6 t^{6} - 1)^{6}) t)

\frac{d t}{d t} = 1

\frac{d}{d t} ((6 t^{6} - 1)^{6}) = 216 t^{5} (6 t^{6} - 1)^{5}

= - 2 (1 \cdot (6 t^{6} - 1)^{6} + 216 t^{5} (6 t^{6} - 1)^{5} t)

化简

- 2 (1 \cdot (6 t^{6} - 1)^{6} + 216 t^{5} (6 t^{6} - 1)^{5} t) : - 2 ((6 t^{6} - 1)^{6} + 216 t^{6} (6 t^{6} - 1)^{5})

= - 2 ((6 t^{6} - 1)^{6} + 216 t^{6} (6 t^{6} - 1)^{5})

l a pl a ce t r an s f or m e^{- 6 t}

\int - \frac{k}{m} d t

\int arccos (a x) d x

\frac{d}{d x} (\frac{cos ( 2 x )}{sin ( 4 x )})

x \to 0 - lim (\frac{1}{1 - 2 ^{\frac{1}{x}}})