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

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

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