An example that my teacher did was:

y=2x(√(r^{2}-x^{2})

Then the derivative would be:

y'=2x((1/2)(r^{2}-x^{2})^{(-1/2)}(-2x))+(r^{2}-x^{2})^{(1/2)}(2)

So what I understand is that he took the derivative inside, then added the derivative of the outside times inside

But I'm confused where he got the -2x from, inside the parenthesis,can someone explain?

Chain rule and product rule is kind of my worst,does anyone know a good and simple rule to follow for chain rule?or someway to kind of explain the chain rule a bit, because it's kind of confusing, especially with a fraction exponent.

Like for example, what I use for the quotient rule is (low d high) - (high d low) over the denominator square it goes.

So it's denominator * derivative of numerator - numerator * derivative of denominator, divided by denominator squared.

So if anyone know a good rhyme or a good simple way to remember the chain rule, and product rule as well, think you can share it to me as well? Thanks