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

Front

Differentiate: f(x) = (x^6 + 4)^5

Back

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

Front

Differentiate: y = (2x + 1)^10

Back

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

Front

When do you use the Chain Rule?

Back

Use the Chain Rule when differentiating a composite function, where one function is nested inside another.

Front

What is the Power Rule?

Back

The Power Rule states that if f(x) = x^n, then f'(x) = n*x^(n-1).

Front

Differentiate: f(x) = x^7(5 + 8x)^3

Back

f '(x) = 24x^7(5 + 8x)^2 + 7x^6(5 + 8x)^3.

Front

What is the Product Rule?

Back

The Product Rule is used to differentiate products of two functions. If u(x) and v(x) are functions, then (uv)' = u'v + uv'.

Front

What is the Quotient Rule?

Back

The Quotient Rule is used to differentiate the quotient of two functions. If u(x) and v(x) are functions, then (u/v)' = (u'v - uv')/v^2.

Front

Differentiate: f(x) = x^6 + 4

Back

f '(x) = 6x^5.

Front

What is the derivative of a constant?

Back

The derivative of a constant is zero.