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Math Help - Change of variables

  1. #1
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    Change of variables

    He guys,

    I have some questions about change of variables
    I have (d^2y/dx^2)*x+x=0 and want to use the substitution z=x^2
    so dy/dx=(dy/dz)*(dz/dx)=2x*(dy/dx)
    But is this correct (d^2y/dx^2)=4(x^2)*(d^2y/dx^2)

    My second question is, how to make the substitution z=yx in the same equation?

    thanks for the help
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  2. #2
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    Quote Originally Posted by sung View Post
    He guys,

    I have some questions about change of variables
    I have (d^2y/dx^2)*x+x=0 and want to use the substitution z=x^2
    so dy/dx=(dy/dz)*(dz/dx)=2x*(dy/dx)
    But is this correct (d^2y/dx^2)=4(x^2)*(d^2y/dx^2)

    My second question is, how to make the substitution z=yx in the same equation?

    thanks for the help
    \frac{dy}{dx}=\frac{dy}{dz}\ \frac{dz}{dx}=2x\frac{dy}{dz}
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  3. #3
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    thanks
    but is this true
    <br />
(\frac{dy}{dx})^{2}=(\frac{d^{2}y}{dx^{2}}) ?<br />

    so

    <br />
(\frac{d^{2}y}{dx^{2}}) = 4x^{2} (\frac{d^{2}y}{dz^{2}})
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  4. #4
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    Quote Originally Posted by sung View Post
    thanks
    but is this true
    <br />
(\frac{dy}{dx})^{2}=(\frac{d^{2}y}{dx^{2}}) ?<br />

    so

    <br />
(\frac{d^{2}y}{dx^{2}}) = 4x^{2} (\frac{d^{2}y}{dz^{2}})
    No, there is a difference.

    \frac{d^2y}{dx^2} is the second derivative of y with respect to x.

    It's not the same as the square of the first derivative.

    \frac{d^2y}{dx^2}=\frac{d}{dx}\left(\frac{dy}{dx}\  right)=\frac{d}{dx}\left(2x\frac{dy}{dz}\right)

    Use the product rule of differentiation for this.
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