## Nikhil619 2 years ago Find dy/dx if y= tan(cos(e^sqrt(x^2+1)))

1. amistre64

its just an application of chaining a chain ....

2. amistre64

$\frac{d}{dx} f(g(h(k(...(x)))))=f'()~g'()~h'()~k'()~.......x'$

3. Nikhil619

wait what i dont get it..

4. perl

amistre is showing off :D

5. Nikhil619

@amistre64

6. Nikhil619

@perl can u help?

7. amistre64

all this amounts to is chain rule practice .... if you know the chain rule, then its just a matter of keeping a clean record

8. perl

amistre, i dont thats right though

9. perl

|dw:1366900627282:dw|

10. Nikhil619

ok so im new to this ..can u teach me pls?

11. amistre64

there are some cases where the mechanism of a derivative works, but the equation itself is bad .... i dont think this is the case tho

12. Nikhil619

what do u want me to do?

13. Nikhil619

:O

14. perl

|dw:1366900684785:dw|

15. amistre64

y= tan(cos(e^sqrt(x^2+1))) let: f = tan(g) g= cos(h) h = e^j j = sqrt(k) k = x^2+1

16. Nikhil619

ok..

17. amistre64

then find the derivative of each one, and multiply them all together ...

18. Nikhil619

but hw can i take derivative of tan(g)(h)(j)(k) ?

19. amistre64

take the derivative of f take the derivative of g take the derivative of h ... NOT take the derivative of f tan(g)(h)(k)...

20. Nikhil619

ok so i go backwards?

21. amistre64

let: f = tan(g) f' = ??? g= cos(h) g' = ??? h = e^j h' = ??? j = sqrt(k) j' = ??? k = x^2+1 k' = ???

22. amistre64

take them one at a time

23. Nikhil619

ok..so k'=2x and j'= 1/x^1/2 rite?

24. amistre64

correct

25. amistre64

except use the "variable" as in each case; only the last one uses an x

26. amistre64

let: f = tan(g) f' = sec^2(g) g= cos(h) g' = -sin(h) h = e^j h' = j e^j j = sqrt(k) j' = 1/(2sqrt(k)) k = x^2+1 k' = 2x

27. Nikhil619

ok can u wait fr a few moments..ill try solving the whole thing and tell u the answer so u can tell me if its right or wrong?

28. amistre64

i would personally leave it in a "defined" format so that it is cleaner to write up

29. Nikhil619

but tom i have an exam..so there i cant keep it clean..i have 2 give the answer..so ill solve it..would u pls pls check it?

30. amistre64

ill chk it when your done ....

31. Nikhil619

wait..fr e^j shouldnt it be e^j * d/dx of j?

32. amistre64

hmmm, j' e^j yes, but your already solving for j' so thats really just e^j

33. amistre64

the j' is part of the chain rule process, which you are already doing ....

34. amistre64

good eye :)

35. Nikhil619

:D thnx...fr ure help also.. :)