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Need help with these derivatives


New member
Nov 5, 2012
, show that

, show that

, show that

, show that

, show that

I know how to get the first derivatives for all these problems, but I'm having problem getting to these alternate derivative forms. Please help. Thanks.


Staff member
Jan 26, 2012
Hi rainbowbaconz,

Welcome to MHB :)

We usually ask for one problem per thread, so which one shall we start with? Pick one and then show us what you did and we'll help you keep going.



Staff member
Feb 24, 2012
Hello and welcome, rainbowbaconz!

It is to your advantage to show what your thoughts are and/or the work you have so far so that we may specifically address where you may be going astray. This helps you in all future problems of this type, since you will be able "fix" the error in the application of the rules for differentiation.

We want to help you to understand the problems, and then to be able to apply the rules to other problems with success.

And please don't feel afraid to be wrong, no one here will think any less of you. We have all been there, trust me! The only thing to be embarrassed about is to be unsure and not ask for guidance.


Well-known member
Feb 2, 2012
Hello, rainbowbaconz!

The fourth one is elementary . . .

[tex]f(x) \:=\:\dfrac{2x^{\frac{3}{2}} - x^{\frac{5}{2}} + 3\sqrt{x}}{\text{-}\sqrt{x}}[/tex]

[tex]\text{Show that: }\:f'(x) \:=\:2(x-1)[/tex]

$\text{We have: }\:f(x) \;=\;\dfrac{2x^{^{\frac{3}{2}}} - x^{^{\frac{5}{2}}} + 3x^{^{\frac{1}{2}}}}{\text{-}x^{^{\frac{1}{2}}}} $

. . . . . . . $ f(x)\;=\;\dfrac{2x^{\frac{3}{2}}}{\text{-}x^{\frac{1}{2}}} - \dfrac{x^{\frac{5}{2}}}{\text{-}x^{\frac{1}{2}}} + \dfrac{3x^{\frac{1}{2}}}{\text{-}x^{\frac{1}{2}}} $

. . . . . . . $f(x) \;=\;\text{-}2x + x^2 - 3$

Hence: ..$f'(x) \;=\;\text{-}2 + 2x \;=\;2(x-1)$


Active member
Oct 16, 2012
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