The secret of success in life is for a man to be ready for his opportunity when it comes. – Benjamin Disraeli

All four cases of Direct Derivative Derivation of rule for direct derivative of algebra function using first principle

$$[f(x) \pm g(x)]’ = f'(x) \pm g'(x)$$
$$[f(x) \times g(x)]’ = f(x) \times g'(x) + g(x) \times f(x)$$
$$\left [ \frac{f(x)}{g(x)} \right ]^’ = \frac{g(x) f'(x) – f(x) g'(x)}{g^2(x)}$$