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Need help with these derivatives

rainbowbaconz

New member
Nov 5, 2012
1
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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.
 

Jameson

Administrator
Staff member
Jan 26, 2012
4,043
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.

Jameson
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
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.
 

soroban

Well-known member
Feb 2, 2012
409
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: ..$f'(x) \;=\;\text{-}2 + 2x \;=\;2(x-1)$
 

alane1994

Active member
Oct 16, 2012
126
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