Question

can you explain the process to finding the derivative of this? y = (x + 1)^2(x^2 + 1)^
-3

Answer 1

Use the product rule.

Answer 2

u = (x+1)^2 u' = 2(x+1)

v = (x^2+1)^-3 v' = -3(x^2+1)^-4

Can you do it now?

Answer 3

No i got that far but it gets complicated for me....

Answer 4

woops, v' = -6x(x^2+1)^-4

Answer 5

complicated !!!!!
let me do it

Answer 6

Or use logarithmic differentiation:
lny = ln( (x + 1)^2(x^2 + 1)^-3)
lny = 2ln(x+1) -3ln(x^2 + 1)
y'/y = 2/(x+1) - 6x/(x^2 + 1)
y' = [2/(x+1) - 6x/(x^2 + 1)] ((x + 1)^2(x^2 + 1)^-3)

Answer 7

y = (x + 1)^2(x^2 + 1)^ -3
y' = [(x + 1)^2][-3(x^2+1)^-4]+[(x^2 + 1)^ -3][2(x+1)]
= -3 (x+1)^2 2x+2
---------- + -------------
(x^2+1)^4 (x^2 + 1)^ 3
= -3 (x+1)^2+ (2x+2)(x^2+1)
------------------------
(x^2+1)^4

Answer 8

logs rule!

Answer 9

simplify it further you'll be getting the answer

Answer 10

Dhashni im doing a study for calc and I got up to the part where you have the 3rd equal sign but how do i simplify it to the the forth part? because thats the answer that I needed to get it right. thanks for everyones help. =)