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Math Help - Finding Derivatives of Functions

  1. #1
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    Finding Derivatives of Functions

    I am working on some homework and am stuck when it comes to problems like these:

    Find ds/dt if s=ln[t^8(t^7-2)]

    Thanks for the help!
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  2. #2
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    Re: Finding Derivatives of Functions

    Where is the problem? Do you know the derivative of ln(u) where u is a function? ...
    You have to use the 'chain rule'.
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    Re: Finding Derivatives of Functions

    I think that u= t^7-2 so therefore the derivative would be 7t^6
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    Re: Finding Derivatives of Functions

    Quote Originally Posted by StarDancer19 View Post
    I am working on some homework and am stuck when it comes to problems like these:

    Find ds/dt if s=ln[t^8(t^7-2)]

    Thanks for the help!
    One way is to use ln(ab)=lna+lnb

    \frac{d}{dt}ln\left[t^8\left(t^7-2\right)\right]=\frac{d}{dt}lnt^8+\frac{d}{dt}ln\left(t^7-2\right)

    x=t^8,\;\;y=t^7-2

    \frac{ds}{dt}=\frac{d}{dt}lnx+\frac{d}{dt}lny

    =\frac{dx}{dt}\;\frac{d}{dx}lnx+\frac{dy}{dt}\; \frac{d}{dy}lny

    You could also first evaluate t^8\left(t^7-2\right)=t^{15}-2t^8
    and work from there.
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  5. #5
    MHF Contributor Siron's Avatar
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    Re: Finding Derivatives of Functions

    What about t^8? ...
    Why not: u=t^8(t^7-2)=t^15-2t^8?
    You know:
    D(ln(u))=D(u)/u

    Can you finish it? ...
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  6. #6
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    Re: Finding Derivatives of Functions

    Yeah, I guess that the t^8 would also be apart of the u. But no, I'm still confused on how to finish it.
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  7. #7
    MHF Contributor Siron's Avatar
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    Re: Finding Derivatives of Functions

    You can follow what Archie meade said or:
    Let u=t^8(t^7-2)=t^15-2t^8
    So:
    D(ln(u))=D(u)/u=(D(t^15-2t^8))(/t^15-2t^8)
    If you can calculate this derivative: D(t^15-2t^8) then you are finished (you can also simplify the fraction).
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