derivative f(x)=(c^5-x^5)/(c^5+c^5)

解答

导数

f (x) = \frac{c ^{5} - x ^{5}}{c ^{5} + c ^{5}}

- \frac{5 x ^{4}}{2 c ^{5}}

求解步骤

\frac{d}{d x} (\frac{c ^{5} - x ^{5}}{c ^{5} + c ^{5}})

将常数提出:

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

= \frac{1}{c ^{5} + c ^{5}} \frac{d}{d x} (c^{5} - x^{5})

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{1}{c ^{5} + c ^{5}} (\frac{d}{d x} (c^{5}) - \frac{d}{d x} (x^{5}))

\frac{d}{d x} (c^{5}) = 0

\frac{d}{d x} (x^{5}) = 5 x^{4}

= \frac{1}{c ^{5} + c ^{5}} (0 - 5 x^{4})

化简

\frac{1}{c ^{5} + c ^{5}} (0 - 5 x^{4}) : - \frac{5 x ^{4}}{2 c ^{5}}

= - \frac{5 x ^{4}}{2 c ^{5}}