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Math Help - Differentiation

  1. #1
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    Differentiation

    Given that y=tan2x and \frac{dy}{dx}=2(1+y^2), show that \frac{d^3y}{dx^2}=4(\frac{dy}{dx})^2 +4y\frac{d^2y}{dx^2}
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: Differentiation

    Quote Originally Posted by Punch View Post
    \frac{dy}{dx}=2(1+y^2)
    Differentiate both sides twice.
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  3. #3
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    Re: Differentiation

    Quote Originally Posted by alexmahone View Post
    Differentiate both sides twice.
    \frac{d^2y}{dx^2}=2(2y)\frac{dy}{dx}

    \frac{d^3y}{dx^2}=4y\frac{d^2y}{dx^2}+\frac{dy}{dx  }(4)

    But the answer has a square for dy/dx
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  4. #4
    MHF Contributor alexmahone's Avatar
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    Re: Differentiation

    Quote Originally Posted by Punch View Post
    \frac{d^2y}{dx^2}=2(2y)\frac{dy}{dx}

    \frac{d^3y}{dx^2}=4y\frac{d^2y}{dx^2}+\frac{dy}{dx  }(4)

    But the answer has a square for dy/dx
    \frac{d^2y}{dx^2}=4y\frac{dy}{dx}

    \frac{d^3y}{dx^2}=4\left(y\frac{d^2y}{dx^2}+\frac{  dy}{dx}\frac{dy}{dx}\right)=4(\frac{dy}{dx})^2+4y \frac{d^2y}{dx^2}
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