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Math Help - Differentiation.

  1. #1
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    Differentiation.

    1) The point at which the slope of the curve y = 2x2 −1 is equal to 2 , is

    2x^2 = 1+2
    x^2=3/2
    x= -1/2 , or x = 1/2



    3). The derivative of y = cos2θ is

    − 2cosθ sinθ


    Moderator edit: Refer forum rule #8: http://www.mathhelpforum.com/math-he...ng-151418.html
    Last edited by mr fantastic; November 5th 2010 at 03:29 AM. Reason: Re-titled, extra questions deleted.
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  2. #2
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    Quote Originally Posted by r-soy View Post
    1) The point at which the slope of the curve y = 2x2 −1 is equal to 2 , is

    2x^2 = 1+2
    x^2=3/2
    x= -1/2 , or x = 1/2
    I'm not sure to which question these particular calculations belong

    The slope of the curve is calculated by the first derivative:

    f(x)=2x^2-1~\implies~f'(x)=\frac{dy}{dx}=4x

    According to he question you are asked to determine the value of x if 4x=2



    ...

    3). The derivative of y = cos2θ is

    − 2cosθ sinθ

    ...
    You forgot to use the chainrule:

    y = \cos(2\theta)~\implies~\frac{dy}{d \theta} = -\sin(2\theta}) \bold{\cdot 2}

    With \sin(2\theta) = 2 \cdot \sin(\theta) \cdot \cos(\theta) you'll get:

    \frac{dy}{dx}=-4 \cdot \sin(\theta) \cdot \cos(\theta)
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