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Math Help - Simple Chain Rule Question

  1. #1
    Newbie
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    Simple Chain Rule Question

    Hello!

    I have a quick question about a question I'm not too sure about...

    y = 2sin^2(x)

    What's the derivative?

    I'm thinking 4sin(x), am I right?
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  2. #2
    Senior Member polymerase's Avatar
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    Quote Originally Posted by lionpants View Post
    Hello!

    I have a quick question about a question I'm not too sure about...

    y = 2sin^2(x)

    What's the derivative?

    I'm thinking 4sin(x), am I right?
    dont forget to chain it....

    y=2sin^2x=2(sin\:x)^2......y'=4(sin\:x)(cos\:x)=2s  in\:2x
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  3. #3
    Super Member
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    London / Cambridge
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    Well you have a chain rule question. So just use the chain rule, don't guess your answers.

    Firstly, the chain rule \frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}

    we have y = 2 \sin^2 x

    so let u = \sin x
    \frac{du}{dx} = \cos x

    y = 2u^2
    \frac{dy}{du} = 4u
    \Rightarrow \frac{dy}{du} = 4 \sin x

    then \frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}
    \Rightarrow \frac{dy}{dx} = 4 \sin x  \cdot  \cos x

    and your done.
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  4. #4
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    Thanks for the help, it helped a lot!

    I have one more question though...

    I have this... y = sin(3x)cos(4x)

    I've worked it out using product rule and chain rule and come out with...

    (3cos(3x) * cos(4x)) + (sin(3x) * -4sin(4x))
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  5. #5
    Math Engineering Student
    Krizalid's Avatar
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    Santiago, Chile
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    It does exist a formula to split the original product into a sum. Have you seen it before?

    Your work is correct.
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