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

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

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

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

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

Solution steps

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

Treat

t

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (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 x^{3} cos (x^{4} + 2) d x

\int_{0}^{3} \frac{3 t}{( t - 4 ) ^{2}} d t

\frac{d}{d x} (2 x + 7 + \frac{450}{x})

f (x) = \frac{2}{3} (x^{2} + 1)^{\frac{3}{2}}

y^{^{''}} + y = 0, y (\frac{π}{3}) = 0, y^{^{'}} (\frac{π}{3}) = 6

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