derivative of ((x^2-5^3)/(125))

解

\frac{d}{d x} (\frac{( x ^{2} - 5 ) ^{3}}{125})

\frac{6 x ( x ^{2} - 5 ) ^{2}}{125}

解答ステップ

\frac{d}{d x} (\frac{( x ^{2} - 5 ) ^{3}}{125})

定数を除去:

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

= \frac{1}{125} \frac{d}{d x} ((x^{2} - 5)^{3})

連鎖法則を適用:

3 (x^{2} - 5)^{2} \frac{d}{d x} (x^{2} - 5)

= 3 (x^{2} - 5)^{2} \frac{d}{d x} (x^{2} - 5)

\frac{d}{d x} (x^{2} - 5) = 2 x

= \frac{1}{125} \cdot 3 (x^{2} - 5)^{2} \cdot 2 x

簡素化

\frac{1}{125} \cdot 3 (x^{2} - 5)^{2} \cdot 2 x : \frac{6 x ( x ^{2} - 5 ) ^{2}}{125}

= \frac{6 x ( x ^{2} - 5 ) ^{2}}{125}