SOLUTION: Hi :o) Last calculus question if anyone can help??? Find derivative of y = (x-1)³(x²-2)² I thought I'd need to use both the product and chain rules, so tried; u=(x-1)³ d

Algebra ->  Rational-functions -> SOLUTION: Hi :o) Last calculus question if anyone can help??? Find derivative of y = (x-1)³(x²-2)² I thought I'd need to use both the product and chain rules, so tried; u=(x-1)³ d      Log On


   



Question 260676: Hi :o)
Last calculus question if anyone can help???
Find derivative of y = (x-1)³(x²-2)²
I thought I'd need to use both the product and chain rules, so tried;
u=(x-1)³ du^n/dx=3(x-1)²(1)
v=(x²-2)² dv^n/dx=2(x²-2)^1(2x)
= {(x-1)³[3(x-1)²(1)]} + {(x²-2)²[2(x²-2)^1(2x)]}
= [(x-1)³3(x-1)²] + [(x²-2)²4x(x²-2)]
= 3(x-1)^5 + 4x(x²-2)^3
...does that look right? Can I go further?
Thanks so, so much again :o)

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
... Start with the given equation


... Derive both sides with respect to x.


... Use the product rule.


... Use the chain rule.

Here's confirmation of the answer.