Derivative of (x²-4)(x²-5) from first principles.
We consider a small increment h in x which creates a corresponding increase k in y.
y+k=(x²+2xh-4)(x²+2xh-5). h² is ignored as insignificantly small.
To find k, we subtract f(x):
In the limit as h,k→0, h/k=dy/dx=4x³-18x. This is the derivative of f(x).