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anonymous

  • 5 years ago

if y = (sin x)^x^2 then differentiate this!!!!! Pls give full steps!!!!!!

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  1. anonymous
    • 5 years ago
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    chane rule

  2. anonymous
    • 5 years ago
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    use d f(x)^g(x)/ dx = f(x)^g(x)d/dx(g(x)log(f(x)) This can be proved easily

  3. anonymous
    • 5 years ago
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    =cos x *2x

  4. anonymous
    • 5 years ago
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    so here i gotta apply the chain rule got it so i have to learn it keep answering ppl i will just go through and then maybe I will be able to understand the solution!!!!

  5. anonymous
    • 5 years ago
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    keep posting what you do!

  6. anonymous
    • 5 years ago
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    ok

  7. anonymous
    • 5 years ago
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    @ruba: not you, I was telling that to tejeshwar so that he may understand and we may correct him if you are wrong

  8. anonymous
    • 5 years ago
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    Tejeshwar: this is not exaclty chain rule, f(x)^g(x) is a bit different thing

  9. anonymous
    • 5 years ago
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    nope sure its chain rule

  10. anonymous
    • 5 years ago
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    First take y=sin(x)^x^2 log(y)=x^2log(sinx) d/dx on both sides so you get, 1/y dy/dx = d/dx (x^2log(sinx)) therefore, dy/dx=y d/dx(x^2log(sin(x))

  11. anonymous
    • 5 years ago
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    \[sin(x)^{x^2}\]?

  12. anonymous
    • 5 years ago
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    ohhhhhhh so so so s o sry mogh im jst 4geting this

  13. anonymous
    • 5 years ago
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    if so take the log, simplify, take the derivative, then multiply by \[sin(x)^{x^2}\]

  14. anonymous
    • 5 years ago
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    ri8 ri8 sat & mogh go on nd bye

  15. anonymous
    • 5 years ago
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    Take this into consideration, y = f(x)^g(x) log y = g(x) log(f(x)) \[(1/y)dy/dx = d/dx(g(x)\log(f(x)))\]

  16. anonymous
    • 5 years ago
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    \[ln(sin(x)^{x^2})=x^2ln(sin(x))\] \[\frac{d}{dx}x^2ln(sin(x))=2xln(sin(x))+\frac{x^2}{x}=2xln(sin(x))+x\] answer: \[(sin(x))^{x^2}(2xln(sin(x))+x)\]

  17. anonymous
    • 5 years ago
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    oops sorry wrong

  18. anonymous
    • 5 years ago
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    \[\frac{d}{dx}x^2ln(sin(x))=2xln(sin(x))+\frac{x^2}{sin(x)}\]

  19. anonymous
    • 5 years ago
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    my mistake. sorry.

  20. anonymous
    • 5 years ago
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    @satellite: d/dx ln(sin(x)) is \[cosx/sinx\]

  21. anonymous
    • 5 years ago
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    wow am i off . you are right and i am wrong!

  22. anonymous
    • 5 years ago
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    two mistakes in one post i should resign.

  23. anonymous
    • 5 years ago
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    lol, it happens!

  24. anonymous
    • 5 years ago
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    btw it is also correct two write \[(sin(x))^{x^2}=e^{x^2ln(sin(x))}\] and differentiate this using the chain rule. the actual work is identical since it all boils down to finding the derivative of \[x^2ln(sin(x))\]CORRECTLY

  25. anonymous
    • 5 years ago
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    just hang on satellite i will just be back 1ce i understand the chain rule!!!!

  26. anonymous
    • 5 years ago
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    Chain rule is easier than it looks, just check out the proof too! Regards.

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