Reflection

This week in calculus we learned section 2.5 and that involved implicit derivatives, explicit, and second derivative with implicit. An explicit function is solved for y, and an implicit is not solved for y. When you take a derivative you must put the notation dy/dx by any variable except for x.
STEPS:
1) Differentiate both sides with respect to x. d_/dx
2) Collect all dy/dx terms on one side, and move the other terms to the other side.
3) Factor out dy/dx.
4) Solve for dy/dx.
5) Simplify, *replace with original equation if possible.**

Examples:

1) x^2 + y^2 = 9
2x + 2ydy/dx = 0
2ydy/dx = -2x
dy/dx = -2x/2y
= -x/y

2) x^3 + y^3 = 64
3x^2 + 3y^2dy/dx = 0
3y^2dy/dx = -3x^2
dy/dx = -3x^2/3y^2
= -x^2/y^2

In section 2.6 we learned about related rates, and you must follow the guidelines from page 150 in the text book to solve these types of problems.

Example:

1) y = 4(x^2 - 5x)
1. dy/dt = ? x = 3 dx/dt = 2
2. y = 4(2x - 5)
3. dy/dt = 4(2x - 5)
4. dy/dt = 4(2(3) - 5)
= 4(6 - 5)
= 4