# Thread: fucction that I don't know how to differentiate

1. ## fucction that I don't know how to differentiate

Differentiate the following function.

g ' (u) =

[LEFT]Attempt
I don't know how I got it wrong this time
I did
= 3u^(1/2)+2u^(1/2)
= 1.5u^(-1/2)+u(-1/2)
= (3/2)u^(-1/2)+u^(-1/2)
= 1/(3/2)u^(1/2)+1/(u^(1/2)
= 1/(sqrt(3/2)u) + 1/(sqrt(u))

I just learnt that x^-1/2 = 1/x^1/2

I don't understand what I did wrong this time Please help me out! thank you so much!

2. Originally Posted by miss.strw
Differentiate the following function.

g ' (u) =

[LEFT]Attempt
I don't know how I got it wrong this time
I did
= 3u^(1/2)+2u^(1/2)
= 1.5u^(-1/2)+u(-1/2)
= (3/2)u^(-1/2)+u^(-1/2)
= 1/(3/2)u^(1/2)+1/(u^(1/2)
= 1/(sqrt(3/2)u) + 1/(sqrt(u))

I just learnt that x^-1/2 = 1/x^1/2

I don't understand what I did wrong this time Please help me out! thank you so much!
Re-write the term of the function:

$g(u)=\dfrac1{\frac{\sqrt{3}}2 u} + \dfrac1{\sqrt{u}} = \dfrac2{\sqrt{3}} \cdot u^{-1} + u^{-\frac12}$

Then

$g'(u)=(-1) \cdot \dfrac2{\sqrt{3}} \cdot u^{-2} - \dfrac12 \cdot u^{-\frac32}$

That's the first rough version of the derivate. You can simplify this term, so go ahead!