Chain Rule

Front

What is the Chain Rule in calculus?

Back

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).

Front

Find the derivative of f(x) = (x^6 + 4)^5.

Back

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

Front

Find y' for y = e^(5x) + 1.

Back

y' = 5e^(5x).

Front

What is the derivative of a constant?

Back

The derivative of a constant is 0.

Front

If f(x) = g(h(x)), what is the derivative f'(x) using the Chain Rule?

Back

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

Front

What is the derivative of sin(g(x))?

Back

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

Front

What is the derivative of ln(g(x))?

Back

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

Front

How do you differentiate a composite function?

Back

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

Front

What is the derivative of (3x^2 + 2)^4?

Back

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

Front

What is the importance of the Chain Rule in calculus?

Back

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