derivative g(t)= 7/(8t^5)

解答

导数

g (t) = \frac{7}{8 t ^{5}}

- \frac{35}{8 t ^{6}}

求解步骤

\frac{d}{d t} (\frac{7}{8 t ^{5}})

将常数提出:

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

= \frac{7}{8} \frac{d}{d t} (\frac{1}{t ^{5}})

使用指数法则:

\frac{1}{a} = a^{- 1}

= \frac{7}{8} \frac{d}{d t} (t^{- 5})

使用幂法则:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{7}{8} (- 5 t^{- 5 - 1})

化简

\frac{7}{8} (- 5 t^{- 5 - 1}) : - \frac{35}{8 t ^{6}}

= - \frac{35}{8 t ^{6}}

\int 3 sin (6 x) d x

\frac{d ^{2}}{d x ^{2}} (- \frac{x}{y})

y^{^{''}} + 36 y = 6 t^{2}

d er i v a t i v e 5^{x^{3}}

e x p an d \frac{( k ^{2} - x ^{2} ) ^{3}}{x ^{2} + a ^{2}}