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Nikhil619

  • 2 years ago

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

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  1. amistre64
    • 2 years ago
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    its just an application of chaining a chain ....

  2. amistre64
    • 2 years ago
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    \[\frac{d}{dx} f(g(h(k(...(x)))))=f'()~g'()~h'()~k'()~.......x'\]

  3. Nikhil619
    • 2 years ago
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    wait what i dont get it..

  4. perl
    • 2 years ago
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    amistre is showing off :D

  5. Nikhil619
    • 2 years ago
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    @amistre64

  6. Nikhil619
    • 2 years ago
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    @perl can u help?

  7. amistre64
    • 2 years ago
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    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
    • 2 years ago
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    amistre, i dont thats right though

  9. perl
    • 2 years ago
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    |dw:1366900627282:dw|

  10. Nikhil619
    • 2 years ago
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    ok so im new to this ..can u teach me pls?

  11. amistre64
    • 2 years ago
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    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
    • 2 years ago
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    what do u want me to do?

  13. Nikhil619
    • 2 years ago
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    :O

  14. perl
    • 2 years ago
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    |dw:1366900684785:dw|

  15. amistre64
    • 2 years ago
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    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
    • 2 years ago
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    ok..

  17. amistre64
    • 2 years ago
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    then find the derivative of each one, and multiply them all together ...

  18. Nikhil619
    • 2 years ago
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    but hw can i take derivative of tan(g)(h)(j)(k) ?

  19. amistre64
    • 2 years ago
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    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
    • 2 years ago
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    ok so i go backwards?

  21. amistre64
    • 2 years ago
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    let: f = tan(g) f' = ??? g= cos(h) g' = ??? h = e^j h' = ??? j = sqrt(k) j' = ??? k = x^2+1 k' = ???

  22. amistre64
    • 2 years ago
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    take them one at a time

  23. Nikhil619
    • 2 years ago
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    ok..so k'=2x and j'= 1/x^1/2 rite?

  24. amistre64
    • 2 years ago
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    correct

  25. amistre64
    • 2 years ago
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    except use the "variable" as in each case; only the last one uses an x

  26. amistre64
    • 2 years ago
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    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
    • 2 years ago
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    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
    • 2 years ago
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    i would personally leave it in a "defined" format so that it is cleaner to write up

  29. Nikhil619
    • 2 years ago
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    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
    • 2 years ago
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    ill chk it when your done ....

  31. Nikhil619
    • 2 years ago
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    wait..fr e^j shouldnt it be e^j * d/dx of j?

  32. amistre64
    • 2 years ago
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    hmmm, j' e^j yes, but your already solving for j' so thats really just e^j

  33. amistre64
    • 2 years ago
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    the j' is part of the chain rule process, which you are already doing ....

  34. amistre64
    • 2 years ago
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    good eye :)

  35. Nikhil619
    • 2 years ago
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    :D thnx...fr ure help also.. :)

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