## DLS 2 years ago DE help

1. DLS

$y=\log(x^{2}\sqrt{x^{2}+1})$

2. DLS

I got something like this $\frac{1}{x^{2}\sqrt{x^{2}+1}} \times 2\sqrt{x^{2}+1} \times 2x$

3. DLS

@ghazi

4. ghazi

there is a bit of editing you should have used product rule

5. ghazi

for (x^2 sqrt{x^2+1})

6. DLS

how?:o

7. ghazi

$\frac{ d(x^2 \sqrt{x^2+1}) }{ dx }=x^2\frac{ d \sqrt{x^2+1} }{ dx }+\sqrt{x^2+1}*2x$

8. DLS

woah :o thanks

9. ghazi

:) YW

10. DLS

how did you get dx in the denominator?

11. ghazi

you are differentiating with respect to x

12. ghazi

i can write it as$\frac{ d }{ dx }(\sqrt{x^2+1}*x^2)$

13. DLS

oh wait equation is messed up lol just asec

14. DLS

$\frac{dy}{dx}=\frac{dlog(x^{2}\sqrt{x^{2}+1}}{dx^{2}\sqrt{x^{2}+1}} \times \frac{dx^{2} \sqrt{x^{2}+1}}{d \sqrt{x^{2}+1}}$ ..so on

15. ghazi

NO

16. DLS

i do like this,where i didnt diff. wrt. dx

17. DLS

thats how im taught >.>

18. ghazi

you have to differentiate wrt x, you can't diffrentiate wrt to function

19. DLS

wth :/ am i taught wrong :S but i was getting all the answers like this

20. ghazi

differentiation is done wrt to a variable basically differentiation tells us rate of change of one variable wrt to another and function is something that tells us the relation between those two variables so we can never get rate of change wrt to a function

21. DLS

okay..!

22. ghazi

$\frac{ d }{ dx }(\sqrt{x^2+1})*x^2+2x* \sqrt{x^2+1}$

23. DLS

okay...clear!

24. ghazi

cool :D

25. ghazi

$\frac{ d }{ dx } (\sqrt{x^2+1})=\frac{ 1 }{ \sqrt{x^2+1} }*\frac{ d }{ dx }(x^2+1)$

26. ghazi

there will be a factor of -1/2 multiplied in RHS

27. DLS

derivative of sqrt x is 1/2x right :o

28. ghazi

-1/2 x

29. DLS

$\frac{d \sqrt{x}}{dx}= \frac{1}{2 \sqrt{x}}$ does my coaching class suck lol :/

30. DLS
31. ghazi

no they are right let me show you

32. DLS

will it be like this: $\frac{1}{2 \sqrt{x^{2}+1}} \times 2x = \frac{x}{\sqrt{x^{2}+1}}$

33. ghazi

$\frac{ d }{ dx } (x)^{-1/2}= \frac{ -1 }{ 2 }(x)^{-1/2-1}$

34. DLS

so how do we have 2 answers

35. ghazi

no we have one, just be careful in calculating power

36. DLS

okay..

37. DLS

so final answer im getting is

38. DLS

$\frac{1}{x(x^{2}+1}$

39. DLS

$\frac{1}{x^{2} \sqrt{x^{2}+1}} \times \frac{x}{\sqrt{x^{2}+1}}$

40. DLS
41. ghazi

$\frac{ d }{ dx } (\sqrt{x^2+1})=\frac{1 }{ 2 }(\sqrt{x^2+1})^{-3/2}* 2x$ your answer

42. DLS

what did you do

43. ghazi

$\frac{ d }{ dx }(x^n)=nx^{n-1}$ hope you know this formula

44. DLS

oh okay!