The product rule is a formula used in calculus to find the derivative of a product of two functions. It states that the derivative of a product of two functions is equal to the first function times the derivative of the second function, plus the second function times the derivative of the first function.
The product rule is used when finding the derivative of a product of two functions. This could include functions such as f(x)g(x) or h(x)k(x).
Yes, the product rule can be extended to more than two functions. It follows the same pattern, where the derivative of the product of all the functions is equal to the first function times the derivative of the product of the remaining functions, plus the second function times the derivative of the product of the remaining functions, and so on.
The chain rule is a formula used in calculus to find the derivative of a composite function. It states that the derivative of a composite function is equal to the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.
To apply the chain rule, we first identify the outer function and the inner function within a composite function. Then, we find the derivative of the outer function and evaluate it at the inner function, and multiply it by the derivative of the inner function. This gives us the derivative of the composite function.