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Differentials

Differentials. Greg Kelly, Hanford High School, Richland, Washington. additions from :www.letu.edu/people/stevearmstrong/math1903/ Lesson %203.8a. ppt. New Look at. We know that then Recall that dy/dx is NOT a quotient it is the notation for the derivative

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Differentials

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  1. Differentials Greg Kelly, Hanford High School, Richland, Washington additions from :www.letu.edu/people/stevearmstrong/math1903/Lesson%203.8a.ppt

  2. New Look at • We know that • then • Recall that dy/dx is NOT a quotient • it is the notation for the derivative • However … sometimes it is useful to use dy and dx as actual quantities

  3. Let be a differentiable function. The differential is an independent variable. The differential is:

  4. The Differential of y • Consider • Then we can say • this is called the differential of y • the notation is d(f(x)) = f ’(x) * dx • it is an approximation of the actual change of y for a small change of x

  5. Try It Out

  6. Example: Consider a circle of radius 10. If the radius increases by 0.1, approximately how much will the area change? very small change in r very small change in A (approximate change in area)

  7. Assignment • Page 240 • #11-18

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