If d/dx (f(3x^2)) = 7x^4, what is f'(x)?

Answer 1

d/dx (f(3x^2)) = 6x f'(3x^2) = 7x^4

f'(3x^2) = (7/6) x^3

define u = 3x^2, Therefore,

x = (u/3)^(1/2)

And

(7/6) x^3 = (7/6)(u/3)^(3/2)

f'(u) = (7/6)(u/3)^(3/2)

Thus

f'(x) = (7/6)(x/3)^(3/2)