derivative of sqrt(x^4-3x^2+4)

解

\frac{d}{d x} (x^{4} - 3 x^{2} + 4)

\frac{x ( 2 x ^{2} - 3 )}{x ^{4} - 3 x ^{2} + 4}

解答ステップ

\frac{d}{d x} (x^{4} - 3 x^{2} + 4)

連鎖法則を適用:

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

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

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

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

簡素化

\frac{1}{2 x ^{4} - 3 x ^{2} + 4} (4 x^{3} - 6 x) : \frac{x ( 2 x ^{2} - 3 )}{x ^{4} - 3 x ^{2} + 4}

= \frac{x ( 2 x ^{2} - 3 )}{x ^{4} - 3 x ^{2} + 4}