# Thread: Complex Derivative (for me, anyways)

1. ## Complex Derivative (for me, anyways)

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

So I converted it to:

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

Then I took the derivative to get:

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

Then I simplified it to:

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

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

2. Originally Posted by dbakeg00
y=$\displaystyle \frac{3}{2}(\sqrt{x}-\frac{1}{\sqrt{x^5}})+\frac{1}{2}(\frac{1}{\sqrt{x }}-\frac{1}{\sqrt{x^3}})$

So I converted it to:

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

Then I took the derivative to get:

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

Then I simplified it to:

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

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

3. 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:

$\displaystyle \frac{3}{4}(\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{x^5} })+\frac{1}{4}(\frac{15}{\sqrt{x^7}}-\frac{1}{\sqrt{x^3}})$

4. Those are are the same, just in different order.

5. 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.