What is the derivative of sech^2(3x) ?

The derivative of sech^2(3x) is -6sech^2(3x)tanh(3x)

What is the first derivative of sech^2(3x) ?

The first derivative of sech^2(3x) is -6sech^2(3x)tanh(3x)

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

- 6 sech^{2} (3 x) tanh (3 x)

Solution steps

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

Apply the chain rule:

2 sech (3 x) \frac{d}{d x} (sech (3 x))

= 2 sech (3 x) \frac{d}{d x} (sech (3 x))

\frac{d}{d x} (sech (3 x)) = - sech (3 x) tanh (3 x) \cdot 3

= 2 sech (3 x) (- sech (3 x) tanh (3 x) \cdot 3)

Simplify

2 sech (3 x) (- sech (3 x) tanh (3 x) \cdot 3) : - 6 sech^{2} (3 x) tanh (3 x)

= - 6 sech^{2} (3 x) tanh (3 x)

What is the derivative of sech^2(3x) ?
The derivative of sech^2(3x) is -6sech^2(3x)tanh(3x)
What is the first derivative of sech^2(3x) ?
The first derivative of sech^2(3x) is -6sech^2(3x)tanh(3x)