1. What is the Chain Rule?

The chain rule is a formula for computing the derivative of the composition of two or more functions. It's one of the most important rules in differential calculus.

2. How Does the Calculator Work?

The calculator uses the chain rule formula:

Where:

• \( \frac{dy}{du} \) — Derivative of outer function with respect to inner function
• \( \frac{du}{dx} \) — Derivative of inner function with respect to x

Explanation: The chain rule allows us to differentiate composite functions by breaking them down into their component parts.

3. Importance of Chain Rule

Details: The chain rule is essential for differentiating complex functions that are compositions of simpler functions. It's widely used in physics, engineering, economics, and other fields.

4. Using the Calculator

Tips: Enter the outer function (y in terms of u) and the inner function (u in terms of x). The calculator will compute each derivative and apply the chain rule.

5. Frequently Asked Questions (FAQ)

Q1: When should I use the chain rule?
A: Use the chain rule whenever you have a function composed of other functions (e.g., sin(x²), e^(3x), etc.).

Q2: Can the chain rule be extended to more than two functions?
A: Yes, for y = f(g(h(x))), the derivative would be f'(g(h(x))) × g'(h(x)) × h'(x).

Q3: What's the difference between chain rule and product rule?
A: Chain rule is for function composition, while product rule is for multiplication of functions.

Q4: Are there functions where chain rule doesn't apply?
A: Chain rule applies to all differentiable composite functions, but some functions might require special handling.

Q5: How is chain rule related to implicit differentiation?
A: Implicit differentiation often uses the chain rule when differentiating terms involving y with respect to x.