Chain Rule 1

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

When do you use the Chain Rule?

Back

The Chain Rule is used when differentiating composite functions, where one function is nested inside another.

Front

Differentiate y = (3x + 2)^5 using the Chain Rule.

Back

y' = 5(3x + 2)^4 * 3 = 15(3x + 2)^4.

Front

What is the Power Rule in calculus?

Back

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

Front

Differentiate y = x^3 using the Power Rule.

Back

y' = 3x^2.

Front

What is the Product Rule in calculus?

Back

The Product Rule is used to differentiate products of two functions. If y = u*v, then y' = u'v + uv'.

Front

Differentiate y = (2x)(x^2 + 1) using the Product Rule.

Back

y' = (2)(x^2 + 1) + (2x)(2x) = 2x^2 + 2 + 4x^2 = 6x^2 + 2.

Front

What is the Quotient Rule in calculus?

Back

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

Front

Differentiate y = (x^2 + 1)/(x^3) using the Quotient Rule.

Back

y' = [(2x)(x^3) - (x^2 + 1)(3x^2)]/(x^3)^2 = (2x^4 - 3x^4 - 3x^2)/(x^6) = (-x^4 - 3x^2)/(x^6).

Front

What is the relationship between the Chain Rule and the Product/Quotient Rules?

Back

The Chain Rule can be used in conjunction with the Product and Quotient Rules when differentiating functions that are products or quotients of composite functions.