## monroe17 2 years ago help? step by step Find dy/dx

1. monroe17

$y=(12\sqrt[3]{x}-\frac{ 1 }{ 4x }+e^2)$

2. monroe17

I know I should rewrite it out.. 12*x^(1/3) but now I'm stuck..?

3. abb0t

$\sqrt[3]{x} = x^(\frac{ 1 }{ 3 }$ by the property, you subtract 1. So 1/3 - 1 = ? $\frac{ 1 }{ 4x } = \frac{ 1 }{ 4 }x^{-1}$ and $e^2$ is just a constant.

4. abb0t

$x^{\frac{ 1 }{ 3 }}$

5. monroe17

okay, thanks.

6. abb0t

$y' = \frac{ 4 }{ x^{\frac{ 2 }{ 3 } }} - \frac{ 1 }{ 4x^2 }$

7. monroe17

so.. rewritten it's $(12*x^{1/3}-\frac{ 1 }{ 4 }x^{-1}+e^2)$

8. abb0t

sorry, change the - to +.

9. monroe17

ahhh i messed up on the original equation

10. monroe17

$(12\sqrt[3]{x}-\frac{ 1 }{ 4x }+e^2)^7$

11. monroe17

so it's chain rule right?

12. abb0t

It's the same thing. now you apply chain rule.

13. abb0t

$7(4x^{\frac{ -2 }{ 3 }} + \frac{ 1 }{ 4x^2 })^6$

14. monroe17

mm.. the answer is different then that.

15. monroe17

$7(12\sqrt[3]{x}-\frac{ 1 }{ 4x }+e^2)^6(4x^{-2/3}+\frac{ 1 }{4 }x^{-2})$

16. abb0t

oh yeah, you multiply by the deriv again.

17. monroe17

why do you multiply by the derivative?

18. monroe17

oh nevermind haha

19. monroe17

I got it.

20. monroe17

I'm forgetting my simple rulessss! Ahhhh D;

21. abb0t

chain rule states f'(g(x))*g'(x)

22. abb0t

it's all good, i totally 4got chain rule for a moment. im rusty in my math

23. monroe17

thanks so much though ;D

24. Outkast3r09

i remember the chain rule by ths let u equal some function within a function and y=$f(u)$ so you have$y=f(u)$ $\frac{dy}{dx}=\frac{du}{dx}\frac{dy}{du}$ if you remember one party like du/dx or dy/du.... you'll know what you ned to cancel

25. Outkast3r09

|dw:1355374308512:dw|

26. Outkast3r09

$(x-2)^x$

27. monroe17

^ I figured it out lol

28. Outkast3r09

chain rule?

29. Outkast3r09

i've never seen this lol.... suprisingly

30. Outkast3r09

i would've just chain ruled it

31. monroe17

it's x-2^{x}

32. monroe17

=1-2^{x}ln(2)

33. abb0t

wat? Lol

34. monroe17

nothing abb0t lol :)

35. Outkast3r09

is that an integration rule?

36. Outkast3r09

o gahd not the ln way of finding derivatives -.-

37. monroe17

lmao, ya --> ;/

38. abb0t

wait for ODE for differentiation w/ integration.

39. Outkast3r09

what do you mean? i've taken Diff Eq

40. Outkast3r09

suprisingly i've gone all the way through math not seeing anything like that lol

41. Outkast3r09

or i did and it was a longg time ago

42. abb0t

for exact equations. also in PDE. chain rule.

43. Outkast3r09

exact dquations are simple, $Ndy=Mdx$ or i might have the backwards i always seem to do it