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人気のある微分積分 >

derivative of sec^3(2x)

解

\frac{d}{d x} (sec^{3} (2 x))

解

6 sec^{3} (2 x) tan (2 x)

解答ステップ

\frac{d}{d x} (sec^{3} (2 x))

連鎖法則を適用:

3 (sec (2 x))^{2} \frac{d}{d x} (sec (2 x))

= 3 (sec (2 x))^{2} \frac{d}{d x} (sec (2 x))

\frac{d}{d x} (sec (2 x)) = sec (2 x) tan (2 x) \cdot 2

= 3 (sec (2 x))^{2} sec (2 x) tan (2 x) \cdot 2

簡素化

3 sec^{2} (2 x) sec (2 x) tan (2 x) \cdot 2 : 6 sec^{3} (2 x) tan (2 x)

= 6 sec^{3} (2 x) tan (2 x)

グラフ

人気の例

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