The Chain Rule in Calculus

Welcome to the froge-tastic explanation of the chain rule in calculus! The chain rule is a fundamental theorem used to find the derivative of composite functions. 🐸✨

The chain rule can be expressed as:

If a function y = f(g(x)) is the composition of f and g, then the derivative of y with respect to x is:

dy/dx = f'(g(x)) * g'(x)

Example Application

For instance, if you have a function h(x) = (3x^2 + 2)^5, applying the chain rule would involve finding the derivative of the outer function (something to the fifth power) and the inner function (3x^2 + 2).

It goes like this:

• Outer function: u^5, derivative is 5u^4
• Inner function: 3x^2 + 2, derivative is 6x

Thus the derivative h'(x) = 5(3x^2 + 2)^4 * 6x. Amazing!

Explore More

For further froge-related mathematical exploration, you can visit:

• Calculus Froges
• Algebra Fun with Froges
• Geometry and Froges

Feel free to reach out if you encounter any difficulties while calculating! Froge loves helping others. 😊