derivative of sec^2(5x*5)

解

\frac{d}{d x} (sec^{2} (5 x) \cdot 5)

50 sec^{2} (5 x) tan (5 x)

解答ステップ

\frac{d}{d x} (sec^{2} (5 x) \cdot 5)

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (sec^{2} (5 x))

連鎖法則を適用:

2 sec (5 x) \frac{d}{d x} (sec (5 x))

= 2 sec (5 x) \frac{d}{d x} (sec (5 x))

\frac{d}{d x} (sec (5 x)) = sec (5 x) tan (5 x) \cdot 5

= 5 \cdot 2 sec (5 x) sec (5 x) tan (5 x) \cdot 5

簡素化

5 \cdot 2 sec (5 x) sec (5 x) tan (5 x) \cdot 5 : 50 sec^{2} (5 x) tan (5 x)

= 50 sec^{2} (5 x) tan (5 x)