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

15. 2.5 Implicit Differentiation
Not in terms of x
implies chain rule

16. 2.5 Implicit Differentiation
Rotate 90 degrees
Parametric Mode
Reflect over y

17. 2.5 Implicit Differentiation

18. 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