Given the equation
This defines as a function of
.
- Without solving for
show that the derivative
satisfies the equation:
(Assume the derivative
exists.)
- Show that
whenever
. (Assume the second derivative
exists.)
- For this part we differentiate each side with respect to
(keeping in mind that
is a function of
, so we need to use the chain rule to differentiate
).
- Using part (a) we differentiate
to find
,