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PhoenixFire

  • 3 years ago

find dy/dx of y=(sin(x))^x

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  1. lgbasallote
    • 3 years ago
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    ln both sides \[\ln y = x \ln (\sin x)\] do implicit differentiation yada yada...got it?

  2. PhoenixFire
    • 3 years ago
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    Yup. Makes sense. thanks.

  3. lgbasallote
    • 3 years ago
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    so can you do it from here?

  4. PhoenixFire
    • 3 years ago
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    Yes I can... forgot about implicit. Should be good.

  5. lgbasallote
    • 3 years ago
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    great :D

  6. beeqay
    • 3 years ago
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    Phoenix, do you know why we use log differentiation here?

  7. beeqay
    • 3 years ago
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    Phoenix, do you know why we use log differentiation here?

  8. beeqay
    • 3 years ago
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    This would be helpful for the future. \[d/dx (a^b) = 0\] because a and b are just constants. \[d/dx (x^n) = nx^{n-1}\] \[d/dx (f(x)^{g(x)}= \log differentiation\] because it's a function raised to a function.

  9. beeqay
    • 3 years ago
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    n is a constant in the second case.

  10. PhoenixFire
    • 3 years ago
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    Thanks beeqay. Helpful to know that.

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