Find d/dx f(x) if we know that d/dx(f(3x))=x^2?

Question

Find d/dx f(x) if we know that d/dx(f(3x))=x^2

Answer 1

By the chain rule, d/dx(f(3x))= 3 f'(3x) = x^2 ==> f'(3x) = (x^2)/3. Now, if we replace x by x/3, we get

f'(3 *x/3) = f'(x) = d/dx f(x) = ((x/3)^2)/3 = (x^2)/27

Answer 2

i think most people forgot the constant of integration:

d/dx(f(3x))=x^2
f(3x) = x^3/3 + C
f(x) = {(x/3)^3} / 3 + D
f(x) = x^3/81 + D
d/dx f(x) = 3x^2/81 = x^2/27

Answer 3

f'(3X)=x^2 so with Integral we know:
f(3x)=(x^3)/3
now we should find f(x).so we should change "3x" to "x":
f(x)=(x^3)/81 we divide "3x" to 3.
now we have the answer:
f'(x)=(x^2)/27

Answer 4

f(3x)=X^3/3
f(x)=(x/3)^3/3=x^3/81
f'(x)=x^2/27

Answer 5

t=3x
df(t)/dx=(df/dt)(dt/dx)
x^2=3(df/dt)
df/dt=x^2/3
df/dx=(df/dt)(dt/dx)=x^2