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TheChainRule 1.7 OBJECTIVE • Find the composition of two functions. • Differentiate using the Extended Power Rule or the Chain Rule. 2012 Pearson Education, Inc. All rights reserved Slide 1.7-2 1.7TheChainRule THEOREM 7: The Extended Power Rule Suppose that g(x) is a differentiable function of x. Then, for any real number k, dx ég(x)ùk = këg(x)ûk 1 × dx g(x) 2012 Pearson Education, Inc. All rights reserved Slide 1.7-3 1.7TheChainRule Example 1: Differentiate f (x)= 1+ x3 ) . dx(1+ 1 x3 2 = 1(1+ 1 x3 2 1 3x2 = 3x2 (1+ x3 ) 1 2 = 2 3x2 1+ x3 2012 Pearson Education, Inc. All rights reserved Slide 1.7-4 1.7TheChainRule Example 2: Differentiate f (x)= (3x 5) (7 x 10 . Combine Product Rule and Extended Power Rule f¢(x)= (3x 5) 10(7 x) ( 1)+ 4(3x 5) (7 x)0 (3) Simplified: f¢(x)= 2(3x 5) (7 x) (67 21x) 2012 Pearson Education, Inc. All rights reserved Slide 1.7-5 ... - tailieumienphi.vn
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