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    Right I have to differentiate the following:



    It seems so simple to me, but it's got me stumped, I can't remember if I treat it as a compound function, the product rule and set u = cos v, or to do the chain rule.

    all help appreciated.
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    chain rule
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    Chain rule
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    so if my head is on straight I should get:

    



6sin 12x^3

    as the two minuses from -sin and  -12x^3 should cancel out?
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    (Original post by BillV3)
    Right I have to differentiate the following:



    It seems so simple to me, but it's got me stumped, I can't remember if I treat it as a compound function, the product rule and set u = cos v, or to do the chain rule.

    all help appreciated.

     \frac {dy}{dx} =   -6sin(4-3x^4) X -12x^3


    The bit in the bracket after cos (inside function ) stays the same. Using the chain rule, you multiply by the derivitive by the derivitive of the inside function.
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    ye I got that in the end, had a sudden 'hang on a minute its just ........' moment, I'll just blame it on a mind blank, they seem to be happening with alarming frequency these days
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    (Original post by BillV3)
    ye I got that in the end, had a sudden 'hang on a minute its just ........' moment, I'll just blame it on a mind blank, they seem to be happening with alarming frequency these days
    Lol!

    This may make it a bit easier :

       y = 6cos (4-3x^4)

    Let u =  4-3x^4
    Then  \frac {du}{dx} = -12x^3

    So the first equation can be written as :  y = 6 cos (u)

    Now using the chain rule :

     \frac {dy}{dx} = -6sin(u) X  \frac {du}{dx}


     \frac {dy}{dx} = -6sin(u) X  -12x^3

      \frac {dy}{dx} = 72x^3 sin(4-3x^4)
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    ah your final answer seems to match mine, I just didn't have the steps in between, I think my brains trying to tell me it needs a rest when I start trying to do the product rule on that lol.
 
 
 
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