11-21-24 Chain Rule Practice

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' is given by 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 y = cos(5x^4)?

Back

y' = -20x^3 sin(5x^4).

Front

How do you differentiate y = tan(3x^2 + 2)?

Back

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

Front

Find the derivative of y = e^(5x) + 1.

Back

y' = 5e^(5x).

Front

What is the derivative of y = sin(x^3 - 2x)?

Back

y' = (3x^2 - 2) cos(x^3 - 2x).

Front

If f(x) = cos(5x^4), what is f'(x)?

Back

f'(x) = -20x^3 sin(5x^4).

Front

What is the formula for the derivative of a composite function?

Back

If y = f(g(x)), then y' = f'(g(x)) * g'(x).

Front

Differentiate y = ln(x^2 + 1).

Back

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

Front

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

Back

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