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sha0403

  • 3 years ago

find dy/dx for sqrt of (9+ ((x-9)/6)^1/5) ? i don't know how to do this...

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  1. Rosh007
    • 3 years ago
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    I think nesting of differentiation is a good idea.. \[\huge \frac{ d }{ dx } (\sqrt{9+(\frac{ x-9 }{ 6 })^{\frac{ 1 }{ 5 }}})\] \[\huge \frac{ d }{ dx } (x^{n+1}) = (n+1)x^{n}\] then use the chain rule \[\huge \sqrt{x} = x^{\frac{ 1 }{ 2}}\] hope this will assist you

  2. sha0403
    • 3 years ago
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    i still did not get it.. can u teach me in detail?

  3. Rosh007
    • 3 years ago
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    I don't know I will be able to complete, thre is a chance of power failure here.. but let me try

  4. Rosh007
    • 3 years ago
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    ok... as a first we need to know chain rule of differentiation

  5. Rosh007
    • 3 years ago
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    as an example \[\huge \frac{ d }{ dx } (\sqrt{a+x^{n}}) = \frac{ d }{ dx } ({a+x^{n}})^\frac{ 1 }{ 2 }\]

  6. Rosh007
    • 3 years ago
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    a function of x... and find the derivative by function by function using the chain rule...(function by function differntiation)

  7. Rosh007
    • 3 years ago
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    here first function is square root (raised to 1/2) second function of x is \[\large x^{n}\] chain rule states that \[\huge \frac{ d }{ dx }(f(g(x))) = f^{'}(g(x))\times g^{'}(x)\]

  8. Rosh007
    • 3 years ago
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    here in this example square root is f(x) and \[\large x^{n}\] is g(x) Hope that now you can some what understand

  9. sha0403
    • 3 years ago
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    i think i get a little what do u say...

  10. Rosh007
    • 3 years ago
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    so the answer for the example becomes \[\huge (a+x^{n})^{\frac{ -1 }{ 2 }} \times (0+n \times x^{n-1}) \] which is equal to \[\huge (a+x^{n})^{\frac{ -1 }{ 2 }} \times(n \times x^{n-1}) \]

  11. Rosh007
    • 3 years ago
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    hope you under stood... so comming back to your question can you say how many functions are there in your qustion?

  12. sha0403
    • 3 years ago
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    about 2 function?

  13. Rosh007
    • 3 years ago
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    try to figure out what is the functions... and how you can apply chain rule.... and refer example when in doubt... i listd the needed formule in my first reply...(expect chain rule, which is listed in above comments)

  14. Rosh007
    • 3 years ago
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    yes you are right... two functions... I think powerfailure will be happening in a minute :(

  15. sha0403
    • 3 years ago
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    ok..then i try i get 1/2((9+(x-9)/6)^1/5)^-1/2 . 1/30((x-9)/6)^-4/5) its right or not?

  16. Rosh007
    • 3 years ago
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    yes .. it is right......(sorry for late reply) glad you figured out

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