derivative of \sqrt[4]{6x^4-7x^2}

解

\frac{d}{d x} (4 6 x^{4} - 7 x^{2})

\frac{x ( 12 x ^{2} - 7 )}{2 ( 6 x ^{4} - 7 x ^{2} ) ^{\frac{3}{4}}}

解答ステップ

\frac{d}{d x} (4 6 x^{4} - 7 x^{2})

連鎖法則を適用:

\frac{1}{4 ( 6 x ^{4} - 7 x ^{2} ) ^{\frac{3}{4}}} \frac{d}{d x} (6 x^{4} - 7 x^{2})

= \frac{1}{4 ( 6 x ^{4} - 7 x ^{2} ) ^{\frac{3}{4}}} \frac{d}{d x} (6 x^{4} - 7 x^{2})

\frac{d}{d x} (6 x^{4} - 7 x^{2}) = 24 x^{3} - 14 x

= \frac{1}{4 ( 6 x ^{4} - 7 x ^{2} ) ^{\frac{3}{4}}} (24 x^{3} - 14 x)

簡素化

\frac{1}{4 ( 6 x ^{4} - 7 x ^{2} ) ^{\frac{3}{4}}} (24 x^{3} - 14 x) : \frac{x ( 12 x ^{2} - 7 )}{2 ( 6 x ^{4} - 7 x ^{2} ) ^{\frac{3}{4}}}

= \frac{x ( 12 x ^{2} - 7 )}{2 ( 6 x ^{4} - 7 x ^{2} ) ^{\frac{3}{4}}}