Chain Rule Review

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

Front

When should you use the Chain Rule?

Back

You should use the Chain Rule when you have a function that is composed of another function, i.e., when there is a function within a function.

Front

Find dy/dx if y = cos^5(x).

Back

dy/dx = -5cos^4(x)sin(x).

Front

What is the derivative of h(x) = 2(x - 4)^3?

Back

Use the Chain Rule: h'(x) = 2 * 3(x - 4)^2 * 1 = 6(x - 4)^2.

Front

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

Back

Using the Chain Rule: dy/dx = (3x^2 - 2)cos(x^3 - 2x).

Front

What is the Quotient Rule?

Back

The Quotient Rule is used to find the derivative of a function that is the quotient of two other functions. If y = u/v, then dy/dx = (v(du/dx) - u(dv/dx)) / v^2.

Front

What is the Product Rule?

Back

The Product Rule is used to find the derivative of a product of two functions. If y = u*v, then dy/dx = u(dv/dx) + v(du/dx).

Front

What is the Power Rule?

Back

The Power Rule states that if y = x^n, then dy/dx = n*x^(n-1), where n is a constant.

Front

How do you differentiate a composite function?

Back

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

Front

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

Back

Using the Chain Rule: dy/dx = e^(g(x)) * g'(x).