Here is a somewhat similar problem worked out for you, but it is a quotient rather than the product you were given:

Since the given function is a quotient, we must use the quotient rule:

d

dx
ex - e-x

ex + e-x

=
(ex+e-x) (d/dx)(ex-e-x) - (ex-e-x)(d/dx)(ex+e-x)

(ex+e-x)2
=
(ex+e-x)(ex+e-x) - (ex-e-x)(ex-e-x)

(ex+e-x)2
(since the derivative of e-x is -e-x)
=
(e2x+2exe-x+e-2x) - (e2x-2exe-x+e-2x)

(ex+e-x)2
(expanding the terms)
=
2exe-x + 2exe-x

(ex+e-x)2
(because the other terms cancel)
=
4

(ex+e-x)2
(because exe-x = 1)


Just close this window to return to the tutorial.