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The Chain Rule

The Chain Rule. What is to be learned?. How to differentiate a composite function. f(x) = (x + 5) 2. = x 2 + 10x + 25. . f(x) = (x + 5) 7. . y = (2x + 5) 7. remember sin( 2x + 30 ) = 0.8. dy / dx. where A = 2x + 30. sinA = 0.8,. let y= u 7. where u = 2x + 5. dy / du. = 7u 6.

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The Chain Rule

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  1. The Chain Rule

  2. What is to be learned? • How to differentiate a composite function

  3. f(x) = (x + 5)2 = x2 + 10x + 25  f(x) = (x + 5)7

  4. y = (2x + 5)7 remember sin(2x + 30) = 0.8 dy/dx where A = 2x + 30 sinA = 0.8, let y= u7 where u = 2x + 5 dy/du = 7u6 du/dx = 2 = dydu dy/du X du/dx dudx dy/du du/dx = dy/dx = 7u6 2 dy/dx = 14u6

  5. y = (2x + 5)7 remember sin(2x + 30) = 0.8 dy/dx where A = 2x + 30 sinA = 0.8, let y= u7 where u = 2x + 5 dy/du = 7u6 du/dx = 2 = dydu dy/du du/dx dudx dy/du du/dx = dy/dx = 7u6 2 dy/dx = 14u6

  6. y = (2x + 5)7 remember sin(2x + 30) = 0.8 dy/dx where A = 2x + 30 sinA = 0.8, let y= u7 where u = 2x + 5 dy/du = 7u6 du/dx = 2 = dydu dy/du du/dx dudx dy/du du/dx = dy/dx = 7u6 2 dy/dx The Chain Rule = 14u6 = 14(2x+5)6

  7. y = (7x + 2)5 let y= u5 where u = 7x + 2 dy/du = 5u4 du/dx = 7 dy/dx = dy/du du/dx = 5u4 7 dy/dx = 35u4 = 35(7x + 2)4

  8. The Chain RuleFor Type (ax + b)n Key to the chain rule dy/dx = dy/du du/dx

  9. y = (x2 + 2)9 let y= u9 where u = x2 + 2 * dy/du = 9u8 du/dx = 2x dy/dx = dy/du du/dx = 9u8 2x dy/dx = 18x u8 = 18x(x2 + 2)8 from*

  10. Fast Tracking y = (7x + 2)5 let y= u5 where u = 7x + 2 dy/du = 5u4 du/dx = 7 dy/dx = dy/du du/dx =5(7x + 2)4 = 5u4 7 dy/dx derivative of bit in brackets

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