vinaur

I assume you are talking about the chain rule.

Let's say that f(x)=5x+2 while g(x)=x^5, so g(f(x))=(5x+2)^5.

To take the derivative, you would have to raise the polynomial to a power, which can be annoying although pascal's triangle (oh and pyramid) make it easier.

So the chain rule says that d (g(f(x)))/dx = d (g(f(x)))/d (f(x)) * d (f(x))/dx, so d (g(f(x)))/dx = 5*(f(x))^4 * 5 , which in turn equals to 5*(5x+2)^4 * 5.

For simplicity f(x) is usually replaced by u, so the derivative sounds something like this: derivative of g(u) is equal to the derivative of g(u)/du times du/dx.

Hope this sort of clarified things up. I know it's kinda hard to follow all the math when it's written this way, but that's the best I can do (well, I could use webassign, but I'm too lazy).

To put it in the simplest terms that I can think, y is a function of x and so is u, so they can be used interchangeably. You treat u as if it was just a regular y.