Reflection

For my blog this week, i'm going to review chain rule, veritcal asymptotes, and derivatives. To begin, when solving for a vertical asymptote of a graph, you factor out the top and bottom and set the bottom equal to zero.
Examples:
1) f(x) = x^2/x^2-4
= x(x)/(x+2)(x-2)
(x+2)(x-2) = 0
x = -2, 2

2) g(x) = 1/2(x+1)
= 2(x+1) = 0
2x+2 = 0
x = -1

Second, when solving chain rule, you take the derivative from outside in. An easy way to remember how to do this is by saying the formula like this: derivative of outside, recopy inside, multipy by derivative of inside.
Examples:
1) y = cos3x^2
y' = -sin3x^2 X (6x)
= -6xsin(3x^2)

2) g(x) = 3(4-9x)^4
= 12(4-9x)^3 X (-9)
= -108(4-9x)^3

Finally, when solving for derivatives, it is usually a simple process. Derivatives can be solved different ways, sometimes you may have to use the product rule or quotient rule.
Examples:
1) f(x) = 3x^5 + 4x +8
f'(x) = 3(5)x^(5-1) + 4 +0
= 15x^4 + 4

2) f(x) = 3xy + 4x^2
f'(x) = [3x(1) + y(3)] + 8x
= 3x + 3y + 8x
= 11x + 3y