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bmelyk

  • 2 years ago

need someone to walk me through this question, please:

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  1. bmelyk
    • 2 years ago
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    Use the appropriate rule or combination of rules to find the derivative of the function defined below. \[y=2(\sin(6x)+\cos(x^3))^\frac{ 1 }{ 2 }\]

  2. bmelyk
    • 2 years ago
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    not even sure how to start this one. ;( looks like it would the the chain rule of course.

  3. hartnn
    • 2 years ago
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    first what is derivative of x^{1/2} = ?

  4. bmelyk
    • 2 years ago
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    1/2x^-1/2

  5. hartnn
    • 2 years ago
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    we always go from outer function to inner function

  6. hartnn
    • 2 years ago
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    \(y'=2(1/2)(\sin(6x)+\cos(x^3))^\frac{ -1 }{ 2 }d/dx(\sin(6x)+\cos(x^3))\)

  7. bmelyk
    • 2 years ago
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    options for the right answer are: \[a)2*\frac{ \cos(6x)-\sin(x^3) }{ (\sin(6x)+cox(x^3))^1/2 }\] \[b)\frac{ \cos(6x) +\sin(x^3)}{ (\sin(6x)+\cos(x^3))^\frac{ 1 }{ 2 } }\] \[c)\frac{ 12 }{ 6x^\frac{ 1 }{ 2 } }*\cos(6x)-\frac{ 6 }{ \cos(x^3)^\frac{ 1 }{ 2 } }*\sin(x^3)*x^2\] \[d)\frac{ 1 }{ (\sin(6x)^\frac{ 1 }{ 2 }+\cos(x^3))^\frac{ 1 }{ 2 } }\] \[e)\frac{ 6*\cos(6x)-3x^2*\sin(x^3) }{ (\sin(6x)+\cos(x^3))^\frac{ 1 }{ 2 } }\] f) same as e only 2 outside of the fraction. \[g) \frac{ 2 }{ \sin(6x)+\cos(x^3))^1/2 }\] \[h) \frac{ 6 }{ \sin(6x)^\frac{ 1 }{ 2 } }*\cos6x-\frac{ 3 }{ \cos(x^3)^\frac{ 1 }{ 2 } }*\sin(x^3)*x^2\]

  8. hartnn
    • 2 years ago
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    u got my last comment ? how i got that ?

  9. bmelyk
    • 2 years ago
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    and i had that so far.

  10. bmelyk
    • 2 years ago
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    yesi got that.

  11. hartnn
    • 2 years ago
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    so what is d/dx(sin(6x)+cos(x^3)) ?

  12. bmelyk
    • 2 years ago
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    do i use the product rule for sin*6x and cos*x^3?

  13. hartnn
    • 2 years ago
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    there is no product, so NO u can treat them individually also what is d/dx (sin 6x) = ?

  14. bmelyk
    • 2 years ago
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    cos6x

  15. bmelyk
    • 2 years ago
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    -sinx^3

  16. hartnn
    • 2 years ago
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    only ?

  17. hartnn
    • 2 years ago
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    i mean only cos 6x ?

  18. bmelyk
    • 2 years ago
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    times 6?

  19. hartnn
    • 2 years ago
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    u need chain rule here too, right ?

  20. hartnn
    • 2 years ago
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    yes! times 6, because u'll have d/dx(6x)

  21. bmelyk
    • 2 years ago
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    cox6x*6

  22. bmelyk
    • 2 years ago
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    cos6x*6

  23. bmelyk
    • 2 years ago
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    ????

  24. hartnn
    • 2 years ago
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    yup, what about 2nd term ? d/dx (cos (x^3)) = ?

  25. bmelyk
    • 2 years ago
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    -sinx^3(3x^2)

  26. hartnn
    • 2 years ago
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    absolutely correct! u got it :)

  27. hartnn
    • 2 years ago
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    so which option is it ?

  28. bmelyk
    • 2 years ago
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    e??

  29. hartnn
    • 2 years ago
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    put everything together, and u'll get it.

  30. hartnn
    • 2 years ago
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    yes, correct :)

  31. bmelyk
    • 2 years ago
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    awesome!

  32. hartnn
    • 2 years ago
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    i hope chain rule is clearer to u now.....

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