derivative f(x)=(13-x^4)/3

解答

导数

f (x) = \frac{13 - x ^{4}}{3}

- \frac{4 x ^{3}}{3}

求解步骤

\frac{d}{d x} (\frac{13 - x ^{4}}{3})

将常数提出:

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

= \frac{1}{3} \frac{d}{d x} (13 - x^{4})

使用微分加减法定则:

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

= \frac{1}{3} (\frac{d}{d x} (13) - \frac{d}{d x} (x^{4}))

\frac{d}{d x} (13) = 0

\frac{d}{d x} (x^{4}) = 4 x^{3}

= \frac{1}{3} (0 - 4 x^{3})

化简

\frac{1}{3} (0 - 4 x^{3}) : - \frac{4 x ^{3}}{3}

= - \frac{4 x ^{3}}{3}