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Math Help - Simple Differentiation (checking i'm right)

  1. #1
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    Simple Differentiation (checking i'm right)

    Hi,

    I'm just doing a past paper but i don't have the mark scheme would anyone be kind enough to double check my answer:

    Question: Differentiate (e^x)/(sin(x) + cos(x))

    MyAnswer: (e^x(sin(x) + cos(x)) + e^x(cos(x) - sin(x)))/((sin(x) + cos(x))^2)
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  2. #2
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    Seems correct, you can also simplify this
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  3. #3
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    Argh dam it i thought you might be able to - i can't for the life of me see where but it just 'looks' like it should? Could you start me off?
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  4. #4
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    Well for starters in the denominator when you multiply the term
    {(sin(x)+cos(x))}^2
    You can remember the identity sin(x)^2+cos(x)^2 = 1
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  5. #5
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    Quote Originally Posted by aceband and reformatted by Mr F View Post
    Hi,

    I'm just doing a past paper but i don't have the mark scheme would anyone be kind enough to double check my answer:

    Question: Differentiate \frac{e^x}{\sin(x) + \cos(x)}

    MyAnswer: \frac{e^x(\sin(x) + \cos(x)) {\color{red}+} e^x(\cos(x) - \sin(x))}{(\sin(x) + \cos(x))^2}
    The red plus should be a minus.

    There is a common factor in the numerator which leads to considerable simplification (after you fix the mistake). I'd leave the denominator as it is.
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