## amorfide 3 years ago y=3(x+2)² differentiate it please, but do it via substitution method, i can differentiate this but i can not do the substitution method

1. satellite73

the derivative of something squared is two times something, times the deriavtive of something

2. amorfide

LOL i know how to do it i just cant do the whole let u= ...

3. satellite73

or you can multiply out an get \[3(x^2+4x+4)=3x^2+12x+12\]\]

4. amorfide

i know i multiply by the power take one off then multiply by derivative of the inside of bracket but i need the substitution method

5. precal

use chain rule

6. satellite73

then ignore it, it is a crutch. if you know the chain rule it is entirely unnecessary to say \(u=x+2\) \(y=u^2\) etc

7. precal

yes, but I believe those were the given instructions

8. amorfide

i really would love the substitution method explained

9. satellite73

i guess you would say \[u=x+2\] \[y=3u^2\] etc etc, but it is silly

10. amorfide

ahhhh okay, then dy/du=6u then du/dx=1 mutliply then substitute u thank you <3

11. satellite73

you have a composition of functions 1) first add 2 2) then square the result, multiply by 3 inner function can be written as \(u=x+2\) outer as \(y=3u^2\)

12. amorfide

so i substitute u= then y is equal to the new equation with u substituted thank you!

13. satellite73

yes, that is correct you get \[6u=6(x+2)\]

14. precal

do you know the chain rule?

15. precal

Take the derivative of the inside, take the derivative of the outside leave the inside alone

16. precal

|dw:1349725718613:dw|

17. amorfide

i know that wy i was struggling with the substitution method i know how to do it straight away though

18. precal

technically the sub method is the chain rule..