## onegirl 2 years ago Find the derivative with and without using the chain rule. f(x) = (x^3 - 1)^2

1. wio

Do you know how to expand it? \[ (x^3-1)^2 = (x^3-1)(x^3-1) \]

2. onegirl

no

3. onegirl

is that with the chain rule or?

4. wio

This is what is called "multiplication"

5. onegirl

ok

6. onegirl

you factor it right?

7. onegirl

let me try to expand it

8. wio

Now we will use distributive property of multiplication. \[ (x^3-1)(x^3-1) = x^3(x^3-1)-1(x^3-1)=x^6-x^3-x^2+1=x^6-2x^3+1 \]

9. onegirl

ok

10. wio

Now take the derivative.

11. onegirl

ok hold on

12. onegirl

the derivative of x^6 - 2x^3 + 1 right?

13. wio

Yeah.

14. onegirl

i got 6x^2 (x^3 - 1)

15. wio

What is the derivative of \(x^6\)?

16. wio

What is the derivative of \(-2x^3\)?

17. onegirl

its 6x^5

18. onegirl

and -6x^2 for -2x^3

19. onegirl

so it will be 6x^5 - 6x^2 ?

20. wio

Yeah. You don't need to factor it.

21. onegirl

ok

22. onegirl

so that's it?

23. wio

yes

24. onegirl

okay can did we use the chain rule on this one or? no chain rule?

25. onegirl

are u there?

26. onegirl

@wio ?

27. sirm3d

chain rule was not used

28. onegirl

okay thanks

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