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Math Help - How do I differentiate y=(4x^2 - e^2x)sin3x ?

  1. #1
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    How do I differentiate y=(4x^2 - e^2x)sin3x ?

    Hi, I have a seemingly straight forward question but I seem to get lost half way through! how do I differentiate y=(4x^2 - e^2x)sin3x ?

    So far, I think: let y = z.sin3x where z = 4x^2 - e^2x

    then dy/dz = 3x.z.cos3x and dz/dx = 8x - 2e^2x

    I know I have to then apply the chain rule but that's where I go wrong, can anyone help please? Apologies for the format.
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  2. #2
    Super Member Quacky's Avatar
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    Re: How do I differentiate y=(4x^2 - e^2x)sin3x ?

    y=(4x^2 - e^{2x})sin3x

    This would be my approach:

    Let u=4x^2 - e^{2x} and v=sin3x

    \frac{du}{dx}=?

    \frac{dv}{dx}=?

    Then use the product rule:

    \frac{dy}{dx}=u\frac{dv}{dx}+v\frac{du}{dx}
    Last edited by Quacky; October 2nd 2011 at 10:26 AM.
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  3. #3
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    Re: How do I differentiate y=(4x^2 - e^2x)sin3x ?

    Thanks, so du/dx = 8x - (2e^2x)

    and dv/dx = 3cos3x

    therefore, dy/dx = (4x^2 - e^2x)(3cos3x) + (sin3x)(8x - 2e^2x)

    = (12x^2 - 3e^2x)(cos3x) + (8x - 2e^2x)(sin3x)

    I'm not sure how to simplify this further, can someone help?
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