The product rule tells us the derivative of two functions f and g that are multiplied together: (fg)' = fg' + gf'.

In abstract algebra, the product rule is the defining property of a derivation. In this terminology, the product rule states that the derivative operator is a derivation on functions.

What is the Product Rule? Product rule in calculus is a method used to find the derivative of any function given in the form of a product obtained by the multiplication of any two differentiable functions.

Nov 16, 2022 · In this section we will give two of the more important formulas for differentiating functions. We will discuss the Product Rule and the Quotient Rule allowing us to differentiate …

Jul 23, 2025 · The product rule is a technique for determining the derivative of any function that is presented in the form of a product produced by multiplying two differentiable functions.

Nov 18, 2025 · What is the Product Rule? The product rule is a fundamental differentiation technique used when you need to find the derivative of two functions multiplied together. It's one of the …

Learn the Product Rule in calculus step by step with clear explanations, worked examples, common mistakes, and practice questions for beginners.

Apr 12, 2026 · By using the continuity of g (x), the definition of the derivatives of f (x) and g (x), and applying the limit laws, we arrive at the product rule, p ′ (x) = f ′ (x) g (x) + g ′ (x) f (x)

What is the Product rule? The Product rule tells us how to differentiate expressions that are the product of two other, more basic, expressions: d d x [f (x) ⋅ g (x)] = d d x [f (x)] ⋅ g (x) + f (x) ⋅ d d x [g (x)]

The product rule is a formula that is used to find the derivative of the product of two or more functions. Given two differentiable functions, f (x) and g (x), where f' (x) and g' (x) are their respective …