Find f'(x) Two Ways: Product/Quotient Rule & Simplifying

[undrcvrbro]

Homework Statement

Find f '(x) two ways: By using the product or quotient rule, and by simplifying first.
f(x) = ((x^3) + 9)/ (x^3)

Homework Equations

f '(x)= (G(x) * F '(x) - F(x) * G '(x)) / [G(x)^2]

The Attempt at a Solution

f '(x)= (x^3)(3x^2) - (x^3 + 9)(3x^2) / (x^3)^2 Plug into quotient rule
f '(x)= (3x^5) - (3x^5) - (27x^2) / (x^6) Simplify
f '(x)= (-27x^2)/(x^6) Canceled out 3x^5
f '(x)= (-27)/ (x^4) Simplified exponents

The answer in the back of the book is what I have(f '(x)= -27/(x^4) =-27x^-4)

So am I done? Was I supposed to simplify from the original equation for f(x) also? I guess I'm asking what "simplify first" exactly means. Any help is greatly appreciated, thank you!

 

[ircdan]

simplify first probably means,

f(x) = (x^3 + 9)/x^3 = 1 + 9/x^3 = 1 + 9x^(-3),
so f'(x) = -27x^(-4)