Question

Differentiate and simplify. y=(x+1)^4 x (x^2+1)^2?

Answer 1

Would I use the product rule? and how would I write that out?

Answer 2

\[9x^8+32x^7+56x^6+72x^5+70x^4+48x^3+24x^2+8x+1\]

Answer 3

That's the answer? or is that the write out?

Answer 4

answer according to me

Answer 5

u meant to differentiate\[(x+1)^4*x*(x^2+1)^2\]

Answer 6

if yes then this is the answer which i have given u

Answer 7

Just (x+1)^4∗(x2+1)^2

Answer 8

Would I just multiply them out 4 times? for the first parenthesis?

Answer 9

then it is

Answer 10

\[\huge 4(x+1)^3*(x^2+1)^2+4x(x+1)^4*(x^2+1)\]

Answer 11

this hould be the answer!

Answer 12

To be clear, differentiate means finding the derivative right? I'm loss on terms

Answer 13

yes differentiation is finding the derivative

Answer 14

apply product rule!!!

Answer 15

How did you get 4x(x+1)^4?

Answer 16

2.2x.(x+1)^4

Answer 17

I don't get that =/

Answer 18

Wow... Use chain rule and product rule.
\[y=(x+1)^4(x^2+1)^2\]
By product rule,\[\frac{d}{dx}[(x+1)^4(x^2+1)^2]=(x^2+1)^2\frac{d}{dx}(x+1)^4+(x+1)^4\frac{d}{dx}(x^2+1)^2\]By chain rule, i.e. \[\frac{dy(x)}{dx}=\frac{dy(u)}{du}\frac{du}{dx}\]We have\[\frac{d(x+1)^4}{x}=\frac{d(x+1)^4}{d(x+1)}\frac{d(x+1)}{dx}=4(x+1)^3\]and\[\frac{d(x^2+1)^2}{dx}=\frac{d(x^2+1)^2}{d(x^2+1)}\frac{d(x^2+1)}{dx}=2(x^2+1)(2x)=4x(x^2+1)\]Hence\[\frac{dy}{dx}=4(x^2+1)^2(x+1)^3+4x(x+1)^4(x^2+1)\]

Answer 19

Woah. hold on o__O

Answer 20

I don't see why the order has to be mixed up in the answer > <

Answer 21

Just for better appearance and tidier.

Answer 22

So could I write out 4(x+1)^3(x^2+1)?

Answer 23

For factorization, you can do this.

Answer 24

K