Posted by Chelsea on Friday, October 22, 2010 at 6:42pm.
So, I have a bunch of derivative problems for homework and the only resource I have is the textbook, since we don't have notes. I have just started and want to make sure I'm doing them correctly. Our teacher said we do not have to simplify them either, so I'm also confused if I'm stopping at the right point.
1. Y(u)= (u^-2 + u^-3)(u^5 - 2u^2)
So, f(x)= (u^-2 + u^-3)
g(x)= (u^5 - 2u^2)
= (-2u^-3 + -3u^-4)(5u^4 - 4u)
= (-2u^-3 + -3u^-4) * D(5u^4 - 4u) + (5u^4 - 4u) * D(-2u^-3 + -3u^-4)
D(5u^4 - 4u)= 20u^3
D(-2u^-3 + -3u^-4)= 6u^-4 + 12u^-5
2. y = (x + 1)/(x^3 + x - 2)
[(x^3 + x - 2) * D(x + 1) - (x + 1) * D(x^3 + x - 2)]/(x^3 + x - 2)^2
D(x + 1)= x ?
D(x^3 + x - 2)= 4x^2 ?
Please help. I need to understand these, as I have plenty to do!
- Calc- Derivatives - Reiny, Friday, October 22, 2010 at 6:51pm
1. My first-line derivative would be
Y' (u) = (u^-2 + u^-3)(5u^4 - 4u) + (u^5-2u^2)(-2u^-3 - 3u^-4)
If I were testing my students to see if they master the product rule, this is the line I would be looking for.
The rest is "window dressing", that is, simplifying it.
If you want a very simple explanation of the product rule, it would be ...
if y = (u)(v)
then y' = uv' + vu'
2. my first-line derivative of this quotient rule is
y' = [ (x^3+ x - 2)(1) - (x+1)(3x^2 + 1) ]/(x^3+x-2)^2
if y = u/v
then y' = (vu' - uv')/v^2
Answer This Question
More Related Questions
- Studying for Calc - I have a quiz on derivatives coming up and I really want to ...
- Final-Chemistry - I have finals coming up in a week and a half. I know I should ...
- Math - I am having trouble figuring out how to do partial derivatives. I have ...
- Calc - y=ln(x+1) +ln(x-1) find dy/dx I have trouble with this problem since i'm ...
- Calculus - Hi~ Thank you for your help! I was trying to work on a problem about ...
- writing - okay, for homework, we have to list 10-15 songs that could be used as ...
- ethinic - I don't think this is totally a homework question, but maybe someone ...
- English - Hey, Any ideas on how to make your own fairytale? I've already started...
- Writing - Am I using comparatives and superlatives correctly in these sentences...
- Grammar and Composition - Can people just give me a bunch of difficult words ...