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August 30, 2015

Homework Help: Calc- Derivatives

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)

y-prime=
[(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!

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