Expert: Paul Klarreich - 1/27/2010

Question
Hi,
Can you in as many steps as possible calculate this differentiation?:

d/dx sqrt (27 - x^2) divided by sqrt (3)  

Answer
Questioner: miles
Country: United Kingdom
Category: Calculus
Private: No
Subject: calculus
Question: Hi,
Can you in as many steps as possible calculate this differentiation?:

d/dx sqrt (27 - x^2) divided by sqrt (3)
.............................................
I suppose I could make it last about 600-700 steps, but it is almost nap time, so:


d/dx sqrt (27 - x^2) divided by sqrt (3)

Chain rule:  u = 27 - x^2,  du/dx = - 2x

y = sqrt (u) /sqrt (3)

y = u^1/2 /sqrt (3)

dy/du = 1/2sqrt (3) u^-1/2
              1
dy/du = --------------
       2 sqrt (3) u^1/2

              1
dy/du = ------------------
       2 sqrt (3) sqrt(u)


                1
dy/du = -------------------------
       2 sqrt (3) sqrt(27 - x^2)

dy   dy du
-- = -- --
dx   du dx


dy          1
-- = ------------------------- (-2x)
dx   2 sqrt (3) sqrt(27 - x^2)


dy          - x
-- = -------------------------
dx   sqrt (3) sqrt(27 - x^2)

Is that enough steps?