Blog #5

Ok so this week was pretty hard. I'm having a lot of trouble with 2.3 and 2.4 just how to use the quotient rule, and I never seem to get the answers that the book has. And I'm still not sure how and when to use the Chain Rule and what not. Anyways, I'll try to explain to the best of my ability, and hopefully study a lot tonight and do at least halfway decently on the test tomorrow. :/ Ok, to the math.

When you're working with the chain rule and composite functions, you work from the outside in.

The Chain Rule is defined as

d/dx[f(g(x))] = f ' (g(x)) * g'(x)

(derivative of the outside, recopy the inside multiplied by the derivative of the inside)

Example:

2 * 8th root of (9-x^2)

2 * (9-x^2)^(1/8)

2 * (1/8)(9-x^2)^(-7/8) * (-2x)

(-x/2)(9-x^2)^(-7/8)

(((-x)/(2)))/(((9-x^2)^(7/8))/(1))

((-x))/(2(9-x^2)^(7/8)) FINAL ANSWER

I already said what I didn't understand in the top of the blog. Some examples of Chain Rule and quotient rule used in different occasions would be nice, especially with trig functions.