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Math Help - use product rule to differentiate function

  1. #1
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    use product rule to differentiate function

    y= 7x^2 cos3x (with respect to x)

    i got as far as -sin3x and 14x but got stuck here!
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  2. #2
    Bar0n janvdl's Avatar
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    Quote Originally Posted by JontyP View Post
    y= 7x^2 cos3x (with respect to x)

    i got as far as -sin3x and 14x but got stuck here!
    The product rule states that:

    (fg)(x) = f'(x)g(x) + f(x)g'(x)
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  3. #3
    Bar0n janvdl's Avatar
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    Where f is the 7x^2 part and g is the cos 3x part
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  4. #4
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    i am using the other form of that
    if y = u * v
    so dy/dx = u (dv/dx) + v (du/dx)

    and taking it from there. after finding the derivatives

    y = 7 x^2 cos3x

    i found the derivative of cos3x to be -3sin3x but cant get 7x^2 which is confusing
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  5. #5
    Bar0n janvdl's Avatar
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    Quote Originally Posted by JontyP View Post
    i am using the other form of that
    if y = u * v
    so dy/dx = u (dv/dx) + v (du/dx)

    and taking it from there. after finding the derivatives

    y = 7 x^2 cos3x

    i found the derivative of cos3x to be -3sin3x but cant get 7x^2 which is confusing
    Okay you can use that form. (It's the same thing anyway, and you should be able to recognise and use all the ways of writing it)

    I'm taking your word for it that the derivative of cos 3x is -3sin 3x (Although it doesn't seem quite correct...)

    Then:

     \frac{dy}{dx} = u \frac{dv}{dx} + v \frac{du}{dx}

    = (cos \ 3x) (14x) + (-3 sin \ 3x) (7x^2)
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