What is the derivative of (sech(5x)^2) ?

The derivative of (sech(5x)^2) is -10sech^2(5x)tanh(5x)

What is the first derivative of (sech(5x)^2) ?

The first derivative of (sech(5x)^2) is -10sech^2(5x)tanh(5x)

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

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

Solution steps

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

Apply the chain rule:

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)

Simplify

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)

What is the derivative of (sech(5x)^2) ?
The derivative of (sech(5x)^2) is -10sech^2(5x)tanh(5x)
What is the first derivative of (sech(5x)^2) ?
The first derivative of (sech(5x)^2) is -10sech^2(5x)tanh(5x)