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Math Help - Deriving sinusoidal functions rules.. confusion.

  1. #1
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    Deriving sinusoidal functions rules.. confusion.

    I have some confusion relating the chain rule and product rule when differentiating sinusoidal functions compared to when I used the rules comfortably when it was just regular functions. I am aware that the derivative of sinx is cosx, and that the derivative of cosx is -sinx btw.

    Example 1:

    f(x)=sin(sinx)

    Would this be the product rule? If so would it look like:
    f'(x)=(cosx)(sinx)+(sinx)(cosx)

    however the book answer is f'(x)=[cos(sinx)](cosx)

    What am I doing wrong?

    Example 2:

    f(theta)= (-pi/2 sin)(2theta-pi)

    product rule? and would the derivative of -pi/2sin be -pi/2cosx?
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  2. #2
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    Quote Originally Posted by kmjt View Post
    I have some confusion relating the chain rule and product rule when differentiating sinusoidal functions compared to when I used the rules comfortably when it was just regular functions. I am aware that the derivative of sinx is cosx, and that the derivative of cosx is -sinx btw.

    Example 1:

    f(x)=sin(sinx)

    Would this be the product rule? If so would it look like:
    f'(x)=(cosx)(sinx)+(sinx)(cosx)

    however the book answer is f'(x)=[cos(sinx)](cosx)

    What am I doing wrong?

    Example 2:

    f(theta)= (-pi/2 sin)(2theta-pi)

    product rule? and would the derivative of -pi/2sin be -pi/2cosx?
    Dear kmjt,

    For example 1 you have to use the chain rule. The product rule can be used when there are to functions multiplied together. But in this case sin(sinx) is a single function.

    \frac{d}{dx}sin(sinx)=\frac{d}{d(sinx)}sin(sinx)\t  imes{\frac{d}{dx}sinx}=cos(sinx)\times{cosx}

    Hope this will help you to understand.

    P.S; Can you please tell what do you mean by "btw".
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  3. #3
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    btw = by the way, sorry aha
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  4. #4
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    Quote Originally Posted by kmjt View Post
    btw = by the way, sorry aha
    Dear kmjt,

    Thanks. And do you understand you problem now?
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  5. #5
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    Oh nevermind I get it now.. thanks!
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