Reflection

Although we learned plenty of new stuff, I’m going to review some of the old stuff so I don’t forget how to work problems like these. Because with some of the new stuff, you have to understand the old information to work the problems.

Finding derivatives of trig.
1. f(x) = 3cosx - sinx/4
= -3sinx - (4)(cosx) - [(sinx)(0)] / (4)^2
= -3sinx-(4cosx/(4)^2)

2. y = 3x^2secx
= 3x^2secxtanx + (3(2))xsecx
= 3x^2secxtanx + 6xsecx

3. y = 1/2csc2x at (pi/4, 1/2)
= -csc2xcot2x
=> -csc2(pi/4)cot2(pi/4)
= 0rivatives with trig.
Related Rates
+ When solving related rates problems, you must follow the guidelines.
+ Examples:
1) y = squareroot(x)
1. dy/dt = ? x = 4 dx/dt = 3
2. y = squareroot(x)
3. dy/dt = 1/2x^-1/2
4. dy/dt = 1/2(4)^-1/2
= 3/4
2) xy = 4
1. dy/dt = ? x = 8 dx/dt = 10
2. xy = 4
3. xdy/dt + ydx/dt = 0
4. xdy/dt = -10y
= -10y/x
Here are the steps you need to solve for an implicit derivative:
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, and replace with original equation if possible
Example: 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