Complex Derivative (for me, anyways)

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March 17th 2010, 10:34 AM
dbakeg00

Complex Derivative (for me, anyways)

y= $\frac{3}{2}(\sqrt{x}-\frac{1}{\sqrt{x^5}})+\frac{1}{2}(\frac{1}{\sqrt{x }}-\frac{1}{\sqrt{x^3}})$

So I converted it to:

$\frac{3}{2}(x^{1/2}-x^{-5/2})+\frac{1}{2}(x^{-1/2}-x^{-3/2})$

Then I took the derivative to get:

$\frac{3}{2}(\frac{1}{2}x^{-1/2}+\frac{5}{2}x^{-7/2})+\frac{1}{2}(\frac{-1}{2}x^{-3/2}+\frac{3}{2}x^{-5/2})$

Then I simplified it to:

$\frac{3}{4}(x^{-1/2}+5x^{-7/2})+\frac{1}{4}(-x^{-3/2}+3x^{-5/2})$

This doesn't match the answer in the back of the book, does anyone see any errors? Thank You.
March 17th 2010, 10:36 AM
e^(i*pi)

Quote:

Originally Posted by dbakeg00

y= $\frac{3}{2}(\sqrt{x}-\frac{1}{\sqrt{x^5}})+\frac{1}{2}(\frac{1}{\sqrt{x }}-\frac{1}{\sqrt{x^3}})$

So I converted it to:

$\frac{3}{2}(x^{1/2}-x^{-5/2})+\frac{1}{2}(x^{-1/2}-x^{-3/2})$

Then I took the derivative to get:

$\frac{3}{2}(\frac{1}{2}x^{-1/2}+\frac{5}{2}x^{-7/2})+\frac{1}{2}(\frac{-1}{2}x^{-3/2}+\frac{3}{2}x^{-5/2})$

Then I simplified it to:

$\frac{3}{4}(x^{-1/2}+5x^{-7/2})+\frac{1}{4}(-x^{-3/2}+3x^{-5/2})$

This doesn't match the answer in the back of the book, does anyone see any errors? Thank You.

That looks fine to me. Perhaps your book has it in a different notation
March 17th 2010, 10:54 AM
dbakeg00

Quote:

Originally Posted by e^(i*pi)

That looks fine to me. Perhaps your book has it in a different notation

The notation that the book puts the answer in is:

$\frac{3}{4}(\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{x^5} })+\frac{1}{4}(\frac{15}{\sqrt{x^7}}-\frac{1}{\sqrt{x^3}})$
March 17th 2010, 11:03 AM
Plato

Those are are the same, just in different order.
March 17th 2010, 11:29 AM
dbakeg00

Quote:

Originally Posted by Plato

Those are are the same, just in different order.

I see it now. Thank you. I think this book takes unnecessary steps to put its answers in different forms. I don't see any reason to re order those, but that's just me. Thanks again for the help.