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2.5 Implicit Differentiation

2.5 Implicit Differentiation

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2.5 Implicit Differentiation

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  1. 2.5 Implicit Differentiation

  2. Implicit DIfferentiation Previous rules such as the product, quotient, power, and chain were only able to be applied to functions written in explicit form. Explicit form is when y is written as a function of x. When a function is not written explicitly you can either change the function to explicit form or use implicit differentiation. Explicit Form y = 1/x Implicit Form xy =1

  3. 2.5 Implicit Differentiation Solve for y

  4. 2.5 Implicit Differentiation

  5. Take the derivative of each term, with respect to x Bring the dy/dx terms left, all other terms right. Factor out and solve for dy/dx. Slope

  6. 2.5 Implicit Differentiation Can't solve for y... So solve for x. Graph it... Slope

  7. Always use this Tstep

  8. Derivative

  9. 2.5 Implicit Differentiation Degenerate Circle

  10. 2.5 Implicit Differentiation Unit Circle Vertical Tangents

  11. 2.5 Implicit Differentiation Solve for y... ?

  12. 2.5 Implicit Differentiation

  13. 2.5 Implicit Differentiation Not in terms of x implies chain rule

  14. 2.5 Implicit Differentiation Rotate 90 degrees Parametric Mode Reflect over y

  15. 2.5 Implicit Differentiation

  16. 2.5 Implicit Differentiation 2.5/3,5,7,11,13,15,19,21,24,25,29,32,35,38,41,45,49,53,57