What is (\partial)/(\partial t)(sech^2(x-t)) ?

The answer to (\partial)/(\partial t)(sech^2(x-t)) is 2sech^2(x-t)tanh(x-t)

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(\partial)/(\partial t)(sech^2(x-t))

\frac{\partial}{\partial t} (sech^{2} (x - t))

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

Solution steps

\frac{\partial}{\partial t} (sech^{2} (x - t))

Treat

x

as a constant

Apply the chain rule:

2 sech (x - t) \frac{\partial}{\partial t} (sech (x - t))

= 2 sech (x - t) \frac{\partial}{\partial t} (sech (x - t))

\frac{\partial}{\partial t} (sech (x - t)) = sech (x - t) tanh (x - t)

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

Simplify

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

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

\int 6 x^{4} e^{x^{5}} d x

\frac{d}{d x} ((2 x^{2} - 2 x) l e f (x, t) t (x^{2} - 3))

f (x) = (2 + 5 x)^{2}

x \to 0 + lim (\frac{1}{x} - \frac{1}{x ^{2} + x})

\frac{\partial}{\partial x} (x y^{2} - x^{2} y + x y)

What is (\partial)/(\partial t)(sech^2(x-t)) ?
The answer to (\partial)/(\partial t)(sech^2(x-t)) is 2sech^2(x-t)tanh(x-t)