Derivative of f^3(x)?

Question

I am trying to find the derivative of a function to the third power (aka Y^3). I have no idea where to start. Can I assume I am dealing with the equation [ f(x) * f(x) ] * [ f(x) ] and treat [ f(x) * f(x) ] as a brand new function such as g(x)?

Answer 1

Ya.. u cn do that .. but there is a simpler method.

we know that derivative of x^3 is 3 x^2
so, for finding derivative of y^3, it wud be 3 y^2 * derivative of y

so the answer for ur question is 3 f^2(x) f '(x)

Answer 2

we know that :(fog)'=f'(g(x))*g'(x)
for example if y=(2x-1)^3
let f(x)=x^3 and g(x)=2x-1
f'(x)=3x^2 and g'(x)=2
y=fog
so y'=f'(g(x))*g'(x)
y'=3(2x-1)^2*2=6(2x-1)^2
so if we have the power of function the derivative of function is:
y^n
ny^(n-1)*y'
the derivative of a function to the third power is:
3y^2*y'

I hope it was helpfull

Answer 3

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Answer 4

Very simple:
d(f^3(x)) =3*f^2(x)*d(f(x)) =3*f^2(x)*f'(x)