find a formula for?

Question

Find a formula for (f^(n)) (x) for f(x)= 1/(3x^2)

Answer 1

unfortunately both the ans above are wrong

f(x) = (3x^2) ^ (-1)
f(f(x) = f((3x^2)^(-1))
= ((3x^2)^(-1))^-1
= (3x^2)^((-1)^2)

by this analogy f n x = (3x^2)*((-1)^n))
that is 3x^2 when n is even and 1/(3x^2) when n is odd

Answer 2

You can take the powers of factors separately, so this is pretty easy. Write it as (1 / (3x^2))^n = (1^n) / [(3^n)(x^2)^n] = 1 / [(3^n)x^(2n)]. As you can see, 1^n = 1 for any n, and (x^2)^n = x^(2n) because (x^a)^b = x^(ab). You could read the final answer as "1 divided by the quantity 3 to the n power times x to the 2n power."

Answer 3

No need to use any formula, we can directly do the problem.
The answer is: 1/(3^nx^2n).