Answer:
f'(x) = 5[1 + f²(x)]
Step-by-step explanation:
By definition, f'(x) = lim h => 0 {[f(x + h) - f(x)]/h}
This was used, together with the given limits:
lim x => 0 f(x) = 0
lim x => 0 f(x)/x = 5,
to determine the derivative of the given function:
f(x + y) = [f(x) + f(y)]/[1 - f(x)f(y)].
The workings are shown in the attachments.
