derivative of sqrt(x^4-9x^2+16)

解

\frac{d}{d x} (x^{4} - 9 x^{2} + 16)

\frac{x ( 2 x ^{2} - 9 )}{x ^{4} - 9 x ^{2} + 16}

解答ステップ

\frac{d}{d x} (x^{4} - 9 x^{2} + 16)

連鎖法則を適用:

\frac{1}{2 x ^{4} - 9 x ^{2} + 16} \frac{d}{d x} (x^{4} - 9 x^{2} + 16)

= \frac{1}{2 x ^{4} - 9 x ^{2} + 16} \frac{d}{d x} (x^{4} - 9 x^{2} + 16)

\frac{d}{d x} (x^{4} - 9 x^{2} + 16) = 4 x^{3} - 18 x

= \frac{1}{2 x ^{4} - 9 x ^{2} + 16} (4 x^{3} - 18 x)

簡素化

\frac{1}{2 x ^{4} - 9 x ^{2} + 16} (4 x^{3} - 18 x) : \frac{x ( 2 x ^{2} - 9 )}{x ^{4} - 9 x ^{2} + 16}

= \frac{x ( 2 x ^{2} - 9 )}{x ^{4} - 9 x ^{2} + 16}