derivative of arcsinh(5x^3-4x^2+11)

解

\frac{d}{d x} (arcsinh (5 x^{3} - 4 x^{2} + 11))

\frac{15 x ^{2} - 8 x}{25 x ^{6} - 40 x ^{5} + 16 x ^{4} + 110 x ^{3} - 88 x ^{2} + 122}

解答ステップ

\frac{d}{d x} (arcsinh (5 x^{3} - 4 x^{2} + 11))

連鎖法則を適用:

\frac{1}{( 5 x ^{3} - 4 x ^{2} + 11 ) ^{2} + 1} \frac{d}{d x} (5 x^{3} - 4 x^{2} + 11)

= \frac{1}{( 5 x ^{3} - 4 x ^{2} + 11 ) ^{2} + 1} \frac{d}{d x} (5 x^{3} - 4 x^{2} + 11)

\frac{d}{d x} (5 x^{3} - 4 x^{2} + 11) = 15 x^{2} - 8 x

= \frac{1}{( 5 x ^{3} - 4 x ^{2} + 11 ) ^{2} + 1} (15 x^{2} - 8 x)

簡素化

\frac{1}{( 5 x ^{3} - 4 x ^{2} + 11 ) ^{2} + 1} (15 x^{2} - 8 x) : \frac{15 x ^{2} - 8 x}{25 x ^{6} - 40 x ^{5} + 16 x ^{4} + 110 x ^{3} - 88 x ^{2} + 122}

= \frac{15 x ^{2} - 8 x}{25 x ^{6} - 40 x ^{5} + 16 x ^{4} + 110 x ^{3} - 88 x ^{2} + 122}