How do you find the derivative of $f(x)=(x-2)^3$ ?

Question

1556 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-20T13:38:42

It depends on whether you have learned the chain rule yet or not.

With the chain rule:

For $u$ a function of $x$ and $n$ an integer,

$d/dx(u^n) = n u^(n-1) (du)/dx$ .

So, $f'(x) = 3(x-2)^2 * d/dx(x-2)$

$= 3(x-2)^2 * 1 = 3(x-2)^2$ .

Without the chain rule

Expand,

$f(x) = (x+2)^3 = x^3+6x^2+12x+8$ .

So, $f'(x) = 3x^2+12x+12$

How do you find the derivative of f(x)=(x-2)^3f(x)=(x-2)^3?