Differentiate equation with parenthesis I have a problem. I'm studying calculus, but I don't have a good math background, so I have a problem: I don't know well how to differentiate an equation with parenthesis.
The equation is the following:
$f(x) = 25x^3(x-1)^2$
Is it correct to use the Differentiation Product Rule in this way:
$f'(x)=75x^2*(x-1)^2+25x^3*2(x-1)$
or before I have to solve $(x-1)^2$ in this way:
f(x) = $25x^3*(x^2+1-2x)$ and then
     = $25x^5+25x^3-50x^4$
?
Thanks in advance

Yes.  Just think of each sub-expression as a separate function, or possibly a composition of functions.  Then all derivatives can be resolved by application of the product and chain rules.
Example: Think of the sub-expression $x^3$ as the expanded product $x.x.x$.  Applying the product rule yields $x'.x.x + x.x'.x +x.x.x'$ = $1.x.x + x.1.x + x.x.1$ = ... (repacking) = $3x^2$.
Of course, once you hit $sin()$, $log()$, etc., you have to resort to something else.
