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Math Help - Differentiating Trig functions

  1. #1
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    Differentiating Trig functions

    Hi,

    I am revising on "Differentiating Trig functions" and I am stuck on a question I am not so sure about. I understand the rules such as the quotient rule, product rule etc. But for this it's not working out.

    Differentiate y = e^2x cos x

    Thanks.
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  2. #2
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    Hi, for this you need to use the product rule

    y = uv, y' = uv' + u'v.

    in this case u = e^2x and v = cosx

    so u' = 2e^2x and v' = -sinx

    combined this give y' = 2(e^2x)cosx - (e^2x)sinx

    Hope that helps.
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  3. #3
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    Thanks,

    How did you differentiate e^2x?
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  4. #4
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    The rule for differentiating exponentials is:

    if y = e^ax, then y' = ae^ax.
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  5. #5
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    Use the chain rule: with y(x)= 2x, this is f(x)= e^{y}. Its derivative is
    \frac{d e^{2x}}{dx}= \frac{d e^y}{dy}\frac{dy}{dx}
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  6. #6
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    Quote Originally Posted by HallsofIvy View Post
    Use the chain rule: with y(x)= 2x, this is f(x)= e^{y}. Its derivative is
    \frac{d e^{2x}}{dx}= \frac{d e^y}{dy}\frac{dy}{dx}
    Hi HallsofIvy,

    Could you please show me how to work it out following that method. I mean the full question: y = e^2x cos x
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  7. #7
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    I have managed to work it out now.

    Thanks.
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