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    How do i differentiate
    dy/dx(1+x)
    with respect to x?

    what i posted is the first derivative and im trying to find the second derivative but having difficulties on how to differentiate it again
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    (Original post by zetamcfc)
    Product rule.
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    dy/dx + d^2y/dx^2(1+x)
    So U=d/dx and v=dy/dx * (1+x) ?
    I'm not sure what the derivatives of d/dx and dy/dx are though...
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    (Original post by ErniePicks)
    How do i differentiate
    dy/dx(1+x)
    with respect to x?

    what i posted is the first derivative and im trying to find the second derivative but having difficulties on how to differentiate it again
    Use the product rule.

    \frac{d}{dx}\left(\frac{dy}{dx} \right)(1+x) + \frac{d}{dx}(1+x) \frac{dy}{dx}.

    Remember that d/dx(dy/dx) = d^2y/dx^2. i.e: the derivative of the derivative is the second derivative.
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    whoops nvm i did it u=dy/dx and v=(1+x)

    so the derivative wrt x of dy/dx is d^2y/dx^2 but what is the derivative wrt to x for d/dx?
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    (Original post by ErniePicks)
    whoops nvm i did it u=dy/dx and v=(1+x)

    so the derivative wrt x of dy/dx is d^2y/dx^2 but what is the derivative wrt to x for d/dx?
    Well you tell me, surely you're used to differentiating x^1? It's just 1 \times x^{1-1}.
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    (Original post by ErniePicks)
    So U=d/dx and v=dy/dx * (1+x) ?
    I'm not sure what the derivatives of d/dx and dy/dx are though...
    y is a function of x

    \displaystyle K(x) =\frac{dy}{dx} (1+x)

    \displaystyle \frac{d(K(x))}{dx} = \frac{d(\frac{dy}{dx} (1+x))}{dx}

     \frac{d(K(x))}{dx} = \frac{d( \frac{dy}{dx} )}{dx} + \frac{d(x \frac{dy}{dx} )}{dx}

      \frac{d(K(x))}{dx} = \frac{d^2 y}{dx^2} +( \frac{dy}{dx} + x\frac{d^2 y}{dx} )

      \frac{d(K(x))}{dx} = (1+x) \frac{d^2 y}{dx} + \frac{dy}{dx}
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    cheers lads, got another bit that is confusing me. I have t differentiate wrt x

    x^3+3y^2=x(y+x^2)

    Now what i did was expand out the bracket with the x and then differentiate wrt x all of it and got the right answer. My teacher used a different method and got this though which i'm not sure how:

    the RHS went to: x(dy/dx+2x)+y+x^2

    Now i understand that the values inside the x bracket is what the original alues would be if they were differentiated wrt x but unsure about the y and x^2 comes from. Is my method of expanding out the brackets with the x and then differentiating okay to use?
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    (Original post by ErniePicks)

    Now i understand that the values inside the x bracket is what the original alues would be if they were differentiated wrt x but unsure about the y and x^2 comes from. Is my method of expanding out the brackets with the x and then differentiating okay to use?
    Yes, your method is fine. The teacher has simply used the product rule with u = x and v = y + x^2
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    (Original post by Zacken)
    Yes, your method is fine. The teacher has simply used the product rule with u = x and v = y + x^2
    lol yeah i just realised this a few seconds ago
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    (Original post by ErniePicks)
    cheers lads, got another bit that is confusing me. I have t differentiate wrt x

    x^3+3y^2=x(y+x^2)

    Now what i did was expand out the bracket with the x and then differentiate wrt x all of it and got the right answer. My teacher used a different method and got this though which i'm not sure how:

    the RHS went to: x(dy/dx+2x)+y+x^2

    Now i understand that the values inside the x bracket is what the original alues would be if they were differentiated wrt x but unsure about the y and x^2 comes from. Is my method of expanding out the brackets with the x and then differentiating okay to use?
    I'm guessing you could, either method should give you the same answer. I personally think product rule is faster though and in some cases you can't expand the brackets because it's too complicated and it makes it easier to make mistakes. Anyway here's how I did it
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    Oops I see you've realised why haha
 
 
 
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