Mambo Number Nine.

This week in Calculus I stressed, studied, hoped for the best, slightly cried after looking at the exam, took a deep breath, then started the exam. I hoped for the best, and it didn’t turn out so bad. The thing we learned new this week was implicit derivatives. This is really easy, its taking the derivative of a y.

Implict Derivative Steps:
1. take derivative of both sides (they have a equal sign and two variables (like x and y))
2. When you take the derivative of a y, you note it by dy/dx or y’
3. Then you solve for dy/dx or y’

Now, if you feel like being an overachiever, or the problem asks for it, the slope is found by…pluging in a x and y-value.

So, now I’m going to steal an example problem from class.

This is your equationy^3+y^2-5y-x^2=-4
Now, lets just simply take the derivative of both sides
3y^2(dy/dx)+2y(dy/dx)-5(dy/dx)-2x=0
Now, simplify..notice I marked every time I took the derivative of y
3y^2(dy/dx)+2y(dy/dx)-5(dy/dx)=2x
now, begin solving for dy/dxdy/dx(3y^2+2y-5)=2x
still simplifyingggg..dy/dx=2x/3y^2+2y-5
TADAAA. ALL DONE :)

That’s really as good as it gets.

Just make sure that you don’t have to have a dy/dx ONLY behind y terms. For example, in product rule it might look like x(dy/dx) because you have to multiply the first term (x) times the derivative of the second term (y)..Which we know would be one and then noting that you took the derivative of y. Although this is really simple, it’s also really easy to make mistakes. So be sure you are working diligently. Hahah.

The thing I am confused on is finding the tangent line when you’re given the equation of like a circle or something random..it was on the take home tests and the exam..and I just don’t get it. I know how to do the normal way, and I know the steps, I just don’t understand when random decimals and points that make a circle and that nonsense. Anyone can help?