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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

= 2 sech (x) (- sech (x) tanh (x))

Simplify

2 sech (x) (- sech (x) tanh (x)) : - 2 sech^{2} (x) tanh (x)

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

- 72 e^{- 2 x}

\frac{d}{d x} ((6 x^{3} + 7)^{\frac{3}{2}})

5 cos (3 t)

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