derivative of (sech(5x)^2)

解答

\frac{d}{d x} ((sech (5 x))^{2})

- 10 sech^{2} (5 x) tanh (5 x)

求解步骤

\frac{d}{d x} ((sech (5 x))^{2})

使用连锁律:

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

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

\frac{d}{d x} (sech (5 x)) = - sech (5 x) tanh (5 x) \cdot 5

= 2 sech (5 x) (- sech (5 x) tanh (5 x) \cdot 5)

化简

2 sech (5 x) (- sech (5 x) tanh (5 x) \cdot 5) : - 10 sech^{2} (5 x) tanh (5 x)

= - 10 sech^{2} (5 x) tanh (5 x)

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