# 3.3.4 - h'(x) = [f'(x)g(x)-g'(x)f(x) ]/(g(x))^2 Ex:...

This preview shows pages 1–5. Sign up to view the full content.

The Product Rule: If f(x) and g(x) are two functions, then the function h(x)=f(x)g(x) has derivative h'(x) = f'(x)g(x)+g'(x)f(x) Notice: This is a more complicated rule than is required for computing the derivative of a sum or constant multiple. Ex: Let f(x)=x^2. By the power rule, f'(x)=2x. The function can also be written as a product of power functions: f(x)=x*x. Using the product rule, f'(x)=x*1+x*1=2x while d/dx[x]*d/dx[x]=1*1 = 1. Not a reasonable value for the rate of change of x^2. Ex: Suppose h(x)=f(x)*g(x) and that f(2)=1, . .. Ex: Compute h'(x) if h(x)=(15^x)*(3x^4-6x^2) . The Quotient Rule: If f(x) and g(x) are two functions, then the function h(x)=f(x)/g(x) has derivative

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: h'(x) = [f'(x)g(x)-g'(x)f(x) ]/(g(x))^2 Ex: h(x)=(x+1)/(x^7-8x) Lecture 3.3: Product and Quotient Rules New Section 1 Page 1 The Chain Rule If f(x) and g(x) are two functions, then the function h(x)=f(g(x)) has derivative h'(x) = f'(g(x))g'(x) Ex: Compute the derivative of h(x)=2^(7x^2+x) The Chain Rule may need to be used more than once: Ex: Compute the derivative of h(x)=2^[(x+2)^3] New Section 1 Page 2 You may need to use several rules: Ex: Compute the derivative of h(x)=(e^x+2)^3 New Section 1 Page 3 New Section 1 Page 4 New Section 1 Page 5...
View Full Document

## 3.3.4 - h'(x) = [f'(x)g(x)-g'(x)f(x) ]/(g(x))^2 Ex:...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online