## monroe17 Group Title can someone help me step by step? Find the derivative 3x^(2)+e^(2y)=4y+tan(x) one year ago one year ago

1. Operative Group Title

solve for dx right?

2. monroe17 Group Title

dy/dx

3. calculusfunctions Group Title

Have you learned implicit differentiation?

4. monroe17 Group Title

I'm not good at it.

5. calculusfunctions Group Title

It's easy! Let me explain it to you in simple terms without getting wordy. If x and y are on the same side of the equal sign, then we say the function is written implicitly, and call it an implicit function. To find the derivative of an implicit function, take the derivative as you normally would but every time you differentiate y, multiply by dy/dx. Then solve for dy/dx. Example: x² + y³ = 5 2x + 3y²(dy/dx) = 0 3y²(dy/dx) = -2x dy/dx = -2x/3y² Understand @monroe17 ?

6. monroe17 Group Title

I got it :) and when you have both x and y on each side you move the y terms to the left? and x on the right then divide?

7. calculusfunctions Group Title

Yes you isolate dy/dx and then solve for dy/dx. Good, you got it!

8. monroe17 Group Title

for instance with my problem i would subtract 6x from both sides and it ends up on the right side of the equal sign. Then 4 is substracted to the right side.. getting sec^2(x)-6x/2e^(2y)-4?

9. calculusfunctions Group Title

Excellent!!

10. monroe17 Group Title

yay, gosh finally.. imma try it for my next problem and see if i get it right.

11. calculusfunctions Group Title

Sure! I'll be on line for another hour or so, hence if you need anything, let me know.

12. monroe17 Group Title

thanks!

13. calculusfunctions Group Title

Welcome! Good Luck!

14. monroe17 Group Title

opps. I came to a problem.. ;/ my next question is 5y^2=3x^(2)y+e^(x) i did.. 10y(dy/dx)=6x(dy/dx)+e^(x) dy/dx(10y*y)=6x+e^(x) dy/dx=6x+e^(x)/10y*y and that's wrong.. what was my mistake??

15. zepdrix Group Title

Woops! When you took the derivative of the right side, it looks like you didn't apply the product rule on the 3x^2y term! :O

16. monroe17 Group Title

ohhhh okay let me try that again.

17. calculusfunctions Group Title

Exactly as @zepdrix said!

18. calculusfunctions Group Title

@monroe17 remember you only multiply by dy/dx when you take the derivative of y, not every time you write y.

19. monroe17 Group Title

oh i don't ?

20. monroe17 Group Title

I got.. 10y(dy/dx)=3x^2+6x*y+e^(x)

21. calculusfunctions Group Title

Example: x² + 2xy - 4 = 6y 2x + 2y + 2x(dy/dx) = 6(dy/dx) Do you see what I did there?

22. monroe17 Group Title

how do i know which term goes to which side for this problem.

23. Eda2012 Group Title

$5y ^{2} = 3x ^{2}y + e ^{x}$ $10 y \frac{ dy }{ dx} = 3x ^{2 }\frac{ dy }{ dx } + 6xy + e ^{x}$ $\frac{ dy }{ dx } = \frac{ 6xy + e ^{x} }{ 10y - 3x }$

24. calculusfunctions Group Title

You know the product rule for derivatives, right?

25. calculusfunctions Group Title

@Eda2012 I am trying to teach her. I do not appreciate you just posting the solution. How is she supposed to learn to solve problems independently if you just give her the answers?

26. monroe17 Group Title

^thank you! lol

27. monroe17 Group Title

the product rule is f(x)g'(x)+g(x)f'(x) right?

28. calculusfunctions Group Title

Correct! Thus if you have a term of 3x²y for example, then your f = 3x² and g = y. And you multiply by dy/dx iff you differentiate y. Understand?

29. calculusfunctions Group Title

If f = 3x² and g = y, then f ' = 6x and g' = dy/dx Do you see?

30. monroe17 Group Title

so.. 10y(dy/dx)=3x^2(dy/dx)+y(6x)+e^(x) 10y(dy/dx)=3x^(2)+6xy+e^(x)

31. monroe17 Group Title

why does 3x^2 go to the left side? I though you make all x to one side and y's the other?

32. calculusfunctions Group Title

(fg)' = fg' + gf' (3x²y)' = 3x²(dy/dx) + 6xy Do you see your mistake when you differentiated 3x²y on the right side?

33. Eda2012 Group Title

@calculusfunctions sometimes you have to show some works and then explain it...sorry...

34. monroe17 Group Title

oh yeah my bad. I mixed them up.

35. calculusfunctions Group Title

@Eda2012 so you show examples and explain the lessons not just give out the answers. I am a teacher so you really don't need to tell me how to do my job!

36. Eda2012 Group Title

@calculusfunctions ok...next time i won't do it again...sorry

37. calculusfunctions Group Title

@monroe17 do you understand now?

38. monroe17 Group Title

^ calculus it's okay, I ignored it :) why does 3x^2 go to the left side? I though you make all x to one side and y's the other?

39. calculusfunctions Group Title

Because it is 3x²(dy/dx) and you're isolating dy/dx.

40. monroe17 Group Title

... im confused

41. calculusfunctions Group Title

OK Do you want me to show you step by step?

42. monroe17 Group Title

let me look at it real quick.

43. calculusfunctions Group Title

Since @eda2012 already posted the correct solution, go ahead and observe it and then tell me which of her steps confuses you, if any. Alright?

44. monroe17 Group Title

okay, give me a little time

45. calculusfunctions Group Title

Sure! Someone else is asking for my help so I'll go and get them started. You call me when you're ready. Take your time.

46. monroe17 Group Title

I'm sorry that took forever, I had a lab report to complete. But, I re-looked over the problem and it seems to make a little more sense. Thank you so much for your help!