Expert: Paul Klarreich - 3/23/2006

Question
Hello my name Is joshua gesell. I am studying Calculus and am On the chain rule. This is the weirdest concept ever.

I have worked for 4 hours to no avail.
Problem #1 in my book y= x^1/2

I always end up getting 1/2 / x^1/2
PLEASE  OH PLEASE TELL ME IT WILL BE A GOD SEND TELL ME WHAT I AM DOING WRONG! Thank you so much.


Answer
Hi, Josh,

You wrote:
Question:  Hello my name Is joshua gesell. I am studying Calculus and am On the chain rule. This is the weirdest concept ever.

I have worked for 4 hours to no avail.
Problem #1 in my book y= x^1/2

I always end up getting 1/2 / x^1/2
PLEASE OH PLEASE TELL ME IT WILL BE A GOD SEND TELL ME WHAT I AM DOING WRONG! Thank you so much.
---------------------------------------
If THIS is the weirdest thing ever, you must be very young.  

What IS weird, however, is why this exercise is in the Chain Rule section.  It does not use the chain rule.  It is just (what I call) the 'x-to-the-n' rule.

Which says that if

y = x^n

then dy/dx = n x^(n-1)

And so, if

y = x^(1/2),

dy/dx = (1/2) x^(1/2 - 1)

and, since  1/2 - 1 = -1/2,
and since  x^(-1/2) = 1/x^(1/2)

WARNING: THE MATERIAL BELOW MAY CONTAIN FRACTIONS AND OTHER MATERIAL INAPPROPRIATE FOR CERTAIN COMPUTING SYSTEMS.  BE SURE TO VIEW IT IN A FIXED-SIZE FONT, SUCH AS COURIER.


your answer is:

dy    1    1        1
-- = --- ------ = ------
dx    2  x^1/2    2x^1/2

usually written as:
   1
---------
2 sqrt(x)

WHEN YOU REALLY GET TO THE CHAIN RULE, YOU CAN WRITE AGAIN.