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okay so since last week i was retarted and forgot my blog..im making sure this is done. therefore, this week we did a reviewed a little on implicite derivatives and learned about related rates and angle of elevation.

Implicite Derivatives guidelines:

1. involves Xs and Ys
2. a.)take the derivative like normal of both sides.
b.)everytime you take the derivative of y note it with dy/dx or y1.
c.)solve for dy/dx.
3. if you want the slope you must plug into a X and a Y value.

Example: y^3+y^2-5y-x^2=-4
3y^2dy/dx+2ydy/dx-5dy/dx-2x+0
dy/dx(3y^2+2y-5)+2x
dy/dx+2x/3y^2+2y-5

Related Rates:

1. identify all variables and equations.
2. identify what you are looking for.
3. make a sketch and label.
4. write an equation involving your variables. you can only have one unknown so a secondary equation may be given.
5. take the derivative with respect to time.
6. substitute in derivative and slope.

Example: the variables x and y are differentiable functions of t and are related by the equation y=2x^3-x+4, when x=2 dx/dt=1. find dy/dt when x=2.
dy/dt=?
x=2 dx/dt=-1
dy/dt=6x^2dx/dt-dx/dt
dy/dt=6(2)^2(-1)+(1)
dy/dx=-23

Related Rates:

1. Identify the known variables, including rates of change and the rate of change that is to be found.
2. Construct an equation relating the quantities whose rates of change are known to the quantity whose rate of change is to be found.
3. Differentiate both sides of the equation with respect to time (or other rate of change).
4. Substitute the known rates of change and the known quantities into the equation.
5. Solve for the wanted rate of change.

so i can honestly say i am having major problems with implicite derivatives and related rates. i really need help so if someone can explain it to me in a way that i can understand that would help so much.