Homework SoursePlease help I am so confused If Fx f9f5fx where f0 0 and f
Please help I am so confused...
If
F(x) = f(9f(5f(x))),
where
f(0) = 0 and f \'(0) = 1,
find
F \'(0).
If
F(x) = f(9f(5f(x))),
where
f(0) = 0 and f \'(0) = 1,
find
F \'(0).
Solution
F\'(x)=f\'(9f(5f(x)))*(9f(5f(x)))\'= =f\'(9f(5f(x)))*9 (f(5f(x)))\'= =9f\'(9f(5f(x)))*f\'(5f(x))*(5f(x))\'= =9f\'(9f(5f(x)))*f\'(5f(x))*5f\'(x) I applied chain rule several times Hence F\'(0)=9f\'(9f(5f(0)))*f\'(5f(0))*5f\'(0)= 9f\'(0)*f\'(0)*5=45
