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.
Differentiate.
1. Y(u)= (u^2 + u^3)(u^5  2u^2)
So, f(x)= (u^2 + u^3)
g(x)= (u^5  2u^2)
power rule:
= (2u^3 + 3u^4)(5u^4  4u)
product rule:
= (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)
yprime=
[(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 firstline derivative would be
Y' (u) = (u^2 + u^3)(5u^4  4u) + (u^52u^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 firstline derivative of this quotient rule is
y' = [ (x^3+ x  2)(1)  (x+1)(3x^2 + 1) ]/(x^3+x2)^2
in short,
if y = u/v
then y' = (vu'  uv')/v^2
Answer This Question
Related Questions
 Studying for Calc  I have a quiz on derivatives coming up and I really want to ...
 Writing  Am I using comparatives and superlatives correctly in these sentences...
 FinalChemistry  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 BC  Figure out the 35th derivative for xsinx. You have to do a few ...
 Calc  y=ln(x+1) +ln(x1) 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 1015 songs that could be used as ...
 Business Communications  English 101  revised.... just wanted to make sure I ...
 ethinic  I don't think this is totally a homework question, but maybe someone ...
More Related Questions