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

Addition and Subtraction

[f(x) \pm g(x)]’ = f'(x) \pm g'(x)

Multiplication (Product Rule)

[f(x) \times g(x)]’ = f(x) \times g'(x) + g(x) \times f(x)

Division (Quotient Rule)

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