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Math Help - easy derivative question

  1. #1
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    Nov 2009
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    easy derivative question

    I have a small question. I have to take the derivative of
    y=(ln(x)+c)/x
    i know i have to use the quotient rule but i dont know what to do with the derivative of c. Do i turn it into a one or drop ot all together. I am doing a diffyQ problem and that equation has to be a solution of
    (x^2)y'+xy=1
    i keep getting 1+x=1 so i think the "c" is messing me up.
    Thanks for any help that anyone can provide
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  2. #2
    Senior Member
    Joined
    Dec 2008
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    In taking derivatives, constants c become 0 while the independent variable (e.g., x) becomes 1. This expresses the fact that while x changes in direct proportion to a change in itself (by a factor of 1), a constant c simply does not change. In symbols,

    \begin{aligned}<br />
\frac{d}{dx}x&=1\\<br />
\frac{d}{dx}c&=0.<br />
\end{aligned}
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