Let y=(sqrt 6−x) .
Find the differential dy when x=3 and dx=0.4
Find the differential dy when x=3 and dx=0.04

Question

Let y=(sqrt 6−x) . 
Find the differential dy when x=3 and dx=0.4  
Find the differential dy when x=3 and dx=0.04

agent0smith · Answer

First find dy/dx

$$\large y = \sqrt{6-x} = (6-x)^{1/2}$$

anonymous · Answer

the derivative is 1/2(6-x)^-1/2(-1)

agent0smith · Answer

Correct. But write it this way, you'll see why in a moment (i just changed the 1/2 to 0.5 for convenience)
$$\large \frac{ dy }{ dx }=-0.5 (6-x)^{-0.5} $$

Now lets imagine dy/dx is a fraction...

agent0smith · Answer

Multiply both sides by dx to get
$$\Large  dy =-0.5 (6-x)^{-0.5} dx$$

anonymous · Answer

oh and from there  do i plug in the x=3 and the dx right

agent0smith · Answer

Yes! :D

anonymous · Answer

alright let me calculate it

anonymous · Answer

i dont know if i calculate it correctly but i got -1/2sqrt3 for the first one

agent0smith · Answer

Did you multiply by the dx also? dy when x=3 and dx=0.4 http://www.wolframalpha.com/input/?i=+-1%2F2%286-3%29%5E%28-1%2F2%29*0.4 dy when x=3 and dx=0.04 http://www.wolframalpha.com/input/?i=+-1%2F2%286-3%29%5E%28-1%2F2%29*0.04

anonymous · Answer

oh i keep forgetting.. alright

anonymous · Answer

alright i just checked.. thank you hopefully i don't forget later on about the dx

agent0smith · Answer

You're welcome :)