This week we took our exam and learned about implict derivatives. Implict derivatives are not that hard. It is pretty much the things we learned like taking derivatives; it just has new steps.
Implict Derivative Steps:
1. take derivative of both sides (implict derivatives have an = sign)
2. every time you take the derivative of y, you have to note it by dy/dx or y^1
3. solve for dy/dx (you are going to have to take out a dy/dx when solving)
4. If you want the slope you must plug in a x and y-value.
Example:
y^3+y^2-5y-x^2=-4
3y^2(dy/dx)+2y(dy/dx)-5(dy/dx)-2x=0
3y^2(dy/dx)+2y(dy/dx)-5(dy/dx)=2x
dy/dx(3y^2+2y-5)=2x
dy/dx=2x/3y^2+2y-5
I pretty understand everything we have done except optimization. No matter how much I study the steps or do problems, optimization doesn't click. I just get stuck on different problems, and I forget little stuff like whether to plug into an original or derivative equation.
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plug into secondary after taking derivative and solving...to find your other variable.
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