Holiday Reflection

Reviewing before exams:
There are many things which we learned but this is a review on some things we worked on
2.5 Implicit and explicit derivatives
+ explicit-solved for y
+ implicit-not solved for y
+ When you take the derivative, you must put the notation, dy/dx, by any variable
except for x.
+ Examples:
1) x^2 + y^2 = 9
2x + 2ydy/dx = 0
2ydy/dx = -2x
dy/dx = -2x/2y
= -x/y
2) xy = 7
(x)(dy/dx) + (y)(1) = 0
xdy/dx + y = 0
dy/dx = -y/x

Other Examples
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)
= 0