The easiest way to remember the Chain Rule is . So when you are trying to differentiate just the part , let so that . Then (which is where the -2x you were wondering about comes from) and .
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
For the product rule, just remember that each of the two parts "takes a turn" being differentiated while the other is left alone. Furthermore its just like the quotient rule except the negative sign is a positive sign and there is no division by g^2.