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 y = sin(2x^2).

Back

y' = 4x cos(2x^2).

Front

What is the derivative of a constant?

Back

The derivative of a constant is 0.

Front

Find H'(1) if H(x) = 3x^2 + 6x.

Back

H'(1) = 9.

Front

What is the derivative of y = (2x + 1)^{10}?

Back

y' = 20(2x + 1)^{9}.

Front

How do you apply the Chain Rule to find the derivative of composite functions?

Back

To apply the Chain Rule, differentiate the outer function and multiply it by the derivative of the inner function.

Front

What is the derivative of y = e^{g(x)}?

Back

y' = e^{g(x)} * g'(x).

Front

Find the derivative of y = ln(3x^2 + 1).

Back

y' = (6x)/(3x^2 + 1).

Front

What is the significance of the Chain Rule in calculus?

Back

The Chain Rule allows us to differentiate complex functions that are composed of simpler functions.

Front

If y = (x^2 + 1)^5, what is y'?

Back

y' = 10(x^2 + 1)^4 * 2x.