Question

how do I differentiate 4sqrt(u^2+u) ?

Answer 1

with respect to u?

Answer 2

WELCOME TO OPENSTUDY!

Answer 3

i will help ya :)

Answer 4

Oh yes, sorry. It says Differentiate f(u) I have not yet differentiated using roots yet

Answer 5

lol fu

Answer 6

ok so first:

Answer 7

\[\sqrt[4]{u^2+u}\]

Answer 8

so first of all do you know how to simplify the equation?

Answer 9

See this......

Answer 10

@Carissa15 you there?

Answer 11

yes, that makes sense so far

Answer 12

I thought that you add 1/2 to "remove" the root from the equation but then I get lost..

Answer 13

??

Answer 14

So you could then take the derivative of the simplified equation? I didn't know how to simplify and remove the \[\sqrt{u}\] from the equation

Answer 15

O....... sqrt=1/2, 4sqrt=4/2=2. Got it?

Answer 16

cool, thank you :-) much more sense

Answer 17

My pleasure.... Don't forget to add a medal and be a fan. And definitely ask more questions. Will try my best to help!

Answer 18

which would leave me with \[4u^2+2(2u+1)+4u\] as the derivative?

Answer 19

\[\sqrt[4]{u^2+u} \implies (u^2+u)^{1/4}\]
\[\frac{ d }{ du } (u^2+u)^{1/4} = \frac{ 1 }{ 4 }(u^2+u)^{-3/4} \times \frac{ d }{ du }(u^2+u)\] notice we apply the chain rule.

Answer 20

So your derivative should be \[\frac{ 1 }{ 4 }(u^2+u)^{-3/4} (2u+1)\]