## onegirl Group Title Find the derivative with and without using the chain rule. f(x) = (x^2 + 1)^3 one year ago one year ago

1. ingenuus Group Title

$f(x)=(x^2+1)^3=(x^2+1)(x^2+1)(x^2+1)$ $f'(x)=6x(x^2+1)^2$

2. ingenuus Group Title

used only product rule

3. onegirl Group Title

is that using the chain rule?

4. ingenuus Group Title

no. i said i only used product rule.

5. onegirl Group Title

okay

6. zepdrix Group Title

One, do you understand how to find the derivative with using chain rule? You would just take the derivative as is.

7. onegirl Group Title

not 100%

8. onegirl Group Title

okay i'll try doing with the chain rule

9. zepdrix Group Title

Ok :)

10. onegirl Group Title

okay can i post it here and correct me if i i mistake somewhere

11. zepdrix Group Title

k

12. onegirl Group Title

$d/dx ((x^2 + 1)^3) = 3(x^2 + 1)^2 d/dx(x^2 + 1) = 3(d/dx(x^2)(x^2 - 1)^2 = 3(2x)(x^2 = 1)^2 = 6x(x^2 + 1)^2$

13. onegirl Group Title

@zepdrix

14. zepdrix Group Title

I'm not quite sure why it changed from x^2+1 to x^2-1. Was that a typo?

15. onegirl Group Title

i see that it didn't show up all of it but here is the last part 3(2x)(x^2 + 1)^2 = 6x(x^2 + 1)^2

16. onegirl Group Title

yes typo for that one

17. zepdrix Group Title

$\large f'(x)=3(x^2+1)^2\frac{d}{dx}(x^2+1)$$\large f'(x)=3(x^2+1)^2(2x) \qquad \qquad f'(x)=6x(x^2+1)^2$ Ok yah looks good :)

18. onegirl Group Title

thanks!

19. zepdrix Group Title

without chain rule is going to be a little tricky. They want you multiply out your binomial :O oh boy.

20. onegirl Group Title

ohh so the one @ingenuus showed is nto by without chain rule?

21. onegirl Group Title

not*

22. onegirl Group Title

the one ingenuus showed its using the product rule

23. zepdrix Group Title

That's another method for doing it without chain rule. Which involved the product rule with 3 terms. Which is a little bit tricky if you've never seen it before. Product rule with 2 terms is probably what you're used to seeing. I was referring to a different method, multiplying out all the brackets as Wio showed you the last time you posted this. :D

24. onegirl Group Title

Ohhhh okay got you