derivative f(x)=4x^4-1/(4x^4)

解

導関数

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

16 x^{3} + \frac{1}{x ^{5}}

解答ステップ

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

和/差の法則を適用:

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

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

\frac{d}{d x} (4 x^{4}) = 16 x^{3}

\frac{d}{d x} (\frac{1}{4 x ^{4}}) = - \frac{1}{x ^{5}}

= 16 x^{3} - (- \frac{1}{x ^{5}})

簡素化

= 16 x^{3} + \frac{1}{x ^{5}}