What is Product Rule?

When the derivative of product of two or more functions is to be taken, the product rule is applied. The product rule states that if a function is the product of the two functions then the derivative of the function is the sum of the product of the first function and the derivative of the second function, with the product of the second function and the derivative of the first function.

For any given function that is the product of the two functions,

d/dx{f(x)·g(x)} = [g(x) × f'(x) + f(x) × g'(x)]

Product Rule Formula

The product rule formula in calculus is the formula that gives the way to find the differentiation of two functions and the formula for the product rule formula is given as,

Suppose we have f(x) = u(x).v(x) then the differentiation of f(x) is find as,

d/dx{u(x)·v(x)} = [v(x) × u'(x) + u(x) × v'(x)]

Where,

• u(x) and v(x) are the differential functions
• u'(x) is the derivative of u(x)
• v'(x) is the derivative of v(x)

Product Rule is the rule that is used to find the derivative of the function that is expressed as the product of two functions. The product rule in calculus is the fundamental rule and is used to find the derivative of the functions.

Product Rule of the calculus is proved using the concept of limit and derivatives. In this article, we will learn about the Product rule, the product rule formula, its proof, examples, and others in detail in this article.