Product Rule Calculator

🧠 Understanding the Product Rule: The Ultimate Guide

Welcome to the definitive resource for the product rule calculator. Whether you're a calculus student, an engineer, or a math enthusiast, understanding how to differentiate the product of two functions is a fundamental skill. This guide, coupled with our powerful tool, will demystify the process and turn complex problems into simple, manageable steps.

What is the Product Rule? 🤔

In calculus, the product rule is a formula used to find the derivative of a product of two or more functions. The product rule formula is: d/dx [f(x)g(x)] = f'(x)g(x) + f(x)g'(x)

Step-by-Step Example 🚶‍♂️

Let's find the derivative of `h(x) = x² * sin(x)`.

• Identify functions: `f(x) = x²` and `g(x) = sin(x)`.
• Find derivatives: `f'(x) = 2x` and `g'(x) = cos(x)`.
• Apply the formula: `h'(x) = (2x)(sin(x)) + (x²)(cos(x))`.

Expansions of the Product Rule 🌐

The "product rule" concept appears in various mathematical contexts.

Exponents Product Rule 🚀

In algebra, the power of a product rule is `(xy)ᵃ = xᵃ * yᵃ`.

Log Product Rule 🪵

For logarithms, the rule is: `logₐ(xy) = logₐ(x) + logₐ(y)`.

Reverse Product Rule & Integration 🔄

The reverse is Integration by Parts: `∫u dv = uv - ∫v du`, derived directly from the product rule.

Why Use Our Calculator? 🏆

• Step-by-Step Clarity: Learn the process, not just the answer.
• Blazing Fast: All calculations happen instantly in your browser.
• Privacy-Focused: Your data never leaves your device.