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Math Help - help with derivative

  1. #1
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    help with derivative

    I need help with the following expression:

    d/dz (z^2+3i)

    Thank you.
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  2. #2
    Member eXist's Avatar
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    Well just break it up:

    d/dz(z^2) + d/dz(3i)
     = 2z + 0
     = 2z

    In this case 3i is a constant, so the derivative is 0.
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  3. #3
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    Thank you!!!
    What if it were a bit more complicated?
    For example,

    \frac{(z-3i)^2}{(z^2+4)^2}?
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  4. #4
    MHF Contributor arbolis's Avatar
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    Quote Originally Posted by georgel View Post
    Thank you!!!
    What if it were a bit more complicated?
    For example,

    \frac{(z-3i)^2}{(z^2+4)^2}?
    I do not really know.
    I know you can always use the definition, i.e. f'(z)= \lim _{h \to 0} \frac{f(z+h)-f(z)}{h} where f(z)=\frac{(z-3i)^2}{(z^2+4)^2}. Of course h\in \mathbb{C}.
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  5. #5
    Member eXist's Avatar
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    \frac{(z-3i)^2}{(z^2+4)^2}

    If it were something like this, then you can rewrite it as so:

    (z-3i)^2(z^2+4)^{-2}

    From here you apply the product rule. (You'll have a chain rule to apply as well.)
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