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    sin^2 (x) / cos^3 (x)


    Erm... :o:
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    have you come across the quotient rule?

    \frac{sin^2x}{cos^3x}

    let u=sin^2x and v=cos^3x
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    Quotient rule? Or write as \frac{\sin^2x}{cos^2x}\cdot secx=tan^2xsecx and then either use an identity connecting tan and sec or use the product rule.
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    ye i've tried to use thazt method. but i get:

    2cos^4 (x) sin (x) + 3cos^2 (x) sin^3 (x)
    ________________________________ ____________

    cos^6 (X)
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    Quotient rule

    (d/dx)f(x)/g(x)=
    [f'(x)g(x)-g'(x)f(x)]/(g(x)^2)

    Sorry but I suck with LaTex, so if that just looks a mess, look on wikipedia or something for the quotient rule, it's right what they've got written for it.
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    i fully understand the quotient rule..tbh is my answer correct? just not simplified enough??
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    (Original post by FoOtYdUdE)
    ye i've tried to use thazt method. but i get:

    2cos^4 (x) sin (x) + 3cos^2 (x) sin^3 (x)
    ________________________________ ____________

    cos^4 (X)
    (a) Check your denominatoer.
    (b) Cancel out what you can, then take a common factor of the top and remember sin^2+cos^2 =1.
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    answer in textbook =

    sinx(2+sin^2 x)
    _______________
    cos^4 x
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    soz, it was cos^6 x not cos^4 x (denominator)
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    (Original post by DFranklin)
    (a) Check your denominatoer.
    (b) Cancel out what you can, then take a common factor of the top and remember sin^2+cos^2 =1.
    erm..:o:
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    (Original post by FoOtYdUdE)
    erm..:o:
    As uninformative posts go, this scores pretty highly.

    What is the problem?
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    (Original post by DFranklin)
    As uninformative posts go, this scores pretty highly.

    What is the problem?
    Sorry \about this. Hang on.
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    This is my working:

    Is it coreect? Have I gone wrong anywhere??


    (2cosxsinx.cos^3 x - (-3cos^3 x sinx . sin^2 x) ) / ( cos^3 x)^2 )

    = (2 cos^4 x sinx + 3cos^2 x sin^3 x ) / (cos^6 x)
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    (Original post by FoOtYdUdE)
    This is my working:

    Is it coreect? Have I gone wrong anywhere??


    (2cosxsinx.cos^3 x - (-3cos^3 x sinx . sin^2 x) ) / ( cos^3 x)^2 )

    = (2 cos^4 x sinx + 3cos^2 x sin^3 x ) / (cos^6 x)
    Thats fine, just cancel down. Take out common factors, and remember that sin^2 x + cos^2 x = 1
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    As has already been said above, you should really try and simplify expressions before you differentiate them.

    Read up to see how this expression goes to tan^2xsecx
    Which can be found using the product rule.

    Or it cancels even further to (sec^2x - 1)secx = sec^3x - secx
    Which can be found using the chain rule.

    So, would you rather use the chain rule, the product rule, or the quotient rule?
 
 
 
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