derivative of arctan(2x^2-4)

解

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

\frac{4 x}{4 x ^{4} - 16 x ^{2} + 17}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

\frac{1}{( 2 x ^{2} - 4 ) ^{2} + 1} \cdot 4 x : \frac{4 x}{4 x ^{4} - 16 x ^{2} + 17}

= \frac{4 x}{4 x ^{4} - 16 x ^{2} + 17}