Differentiation Formulas

Proposition (Differentiation Formulas) Let be a function.

    (i) If is a constant function, for any real number then
    
    (ii) If is a power function, for any real number , then

    (iii) If for any two functions and then

    (iv) If for any two functions and then

    (v) If for any two functions and , and any two constants and , then

    (vi) If for any two functions and , then

    (vii) If for any two functions and , then

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