Chain Rule

The Chain Rule is a formula for computing the derivative of the composition of two or more functions. It states that if you have a function y = f(g(x)), then the derivative y' = f'(g(x)) * g'(x).

f '(x) = 30x^5(x^6 + 4)^4.

y' = 5e^(5x).

The derivative of a constant is 0.

f'(x) = g'(h(x)) * h'(x).

The derivative is cos(g(x)) * g'(x) using the Chain Rule.

The derivative is (1/g(x)) * g'(x) using the Chain Rule.

Use the Chain Rule: differentiate the outer function and multiply by the derivative of the inner function.

The derivative is 24x(3x^2 + 2)^3.

The Chain Rule is essential for finding derivatives of complex functions, especially in real-world applications.