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Math Help - Finding the derivative

  1. #1
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    Finding the derivative

    Hey there,

    I am having trouble understanding how to work out this question, which is x(x+y)-e^y =y^2

    I have been given the working out, of which the first line is (x+y)+x(1+y^1)-e^y *y^1=2yy^1
    Really not to sure what rules they used to get from a to b, so if anyone could share, that would be most appreciated

    Nettie.L
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  2. #2
    Senior Member MacstersUndead's Avatar
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    Re: Finding the derivative

    Are you differentiating with respect to y or with respect to x?
    Overall, in order to solve the problem you have to have knowledge of what is known as Implicit Differentiation
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  3. #3
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    Re: Finding the derivative

    with respect to y
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  4. #4
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    Re: Finding the derivative

    Do you mean you want to differentiate x with respect to y or y with respect to x? The first is what you said but what you give would be correct if by "y^1" you mean the derivative of y with respect to x, normally written as y'. Solve for y'.
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  5. #5
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    Re: Finding the derivative

    x with respect to y. sorry, I meant y'
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  6. #6
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    Re: Finding the derivative

    the derivative of y w/r to x is y' or dy/dx

    the derivative of x w/r to y is x' or dx/dy

    one more time ... which?
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  7. #7
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    Re: Finding the derivative

    well, in the worked answer they have d/dy (so I'm guessing that means dx/dy). What I really want to know is how they get from that first question, to the (x+y)+x(1+y')-e^y *y'=2yy'
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  8. #8
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    Re: Finding the derivative

    the original is taking the derivative w/r to x , so y is treated as a function of x

    \frac{d}{dx} \left[x(x+y)-e^y =y^2\right]

    product rule with the first term, chain rule w/ the rest ...

    (1)(x+y) + x(1 + y') - e^y \cdot y' = 2y \cdot y'

    the goal now is to algebraically solve for y', the derivative of y w/r to x ...
    Thanks from NettieL
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