What is the chain rule in calculus?

What is the chain rule in calculus?

The chain rule is a formula for computing the derivative of a composite function. It states that if you have two functions, f(g(x)), the derivative is f'(g(x)) * g'(x).

Can you give me an example of how to use the chain rule?

Sure! If you want to differentiate f(x) = (3x + 2)^4, let g(x) = 3x + 2 and f(u) = u^4. The derivative is f'(g(x)) * g'(x) = 4(3x + 2)^3 * 3.

What if I have a more complex function?

For a more complex function like f(x) = sin(2x^2 + 3x), you would set g(x) = 2x^2 + 3x and f(u) = sin(u). The derivative would be cos(g(x)) * g'(x) = cos(2x^2 + 3x) * (4x + 3).

Are there any common mistakes when using the chain rule?

Yes, a common mistake is forgetting to multiply by the derivative of the inner function. Always remember to apply the chain rule correctly!