product rule
[product rule|product rule] is a method for finding the derivative of the product of two functions at a specific point by applying the rule: j'(x) = f'(x)g(x) + f(x)g'(x).
Definition
product rule is a method for finding the derivative of the product of two functions at a specific point by applying the rule: j'(x) = f'(x)g(x) + f(x)g'(x).
Mechanism
product rule The product rule is applied to differentiate terms like xtanx, yielding (1)(tanx) + (sec²x)(x). It also helps compute derivatives such as cscxcotx for cscx, and is used in finding expressions involving siny and x³.
Effects
product rule affects the correctness of statements involving derivatives of products, such as the example where applying it to xe* yields the correct result xe*-e*+C. It also governs the differentiation of products like Fodnt and AC, requiring the sum of individual derivatives multiplied by the other function.