please show all your work in finding the derivitive. Much appreceated!
2006-10-31 22:32:38 · 9 answers · asked by Jac R 3 in Science & Mathematics ➔ Mathematics
SQUARE ROOT!! dont forget that
SQROOT(4-X^2)
2006-10-31 22:41:33 · update #1
oh yeah, basically i'm asking this question because of Critical Numbers.. I need to find the critical numbers for that function!
Help!!!!
2006-10-31 22:48:08 · update #2
I'm so confused with all your different answers!
How do i find the critical numbers for this function?
=[ =[ =[ help!
2006-10-31 22:58:26 · update #3
Even 'tho it's obvious, you really should force yourself to say 'derivative with respect to x' because, later on, it won't be quite so obvious what the derivative is being taken with respect to ☺
First of all √(4-x²) = (4-x²)^½. So
(d/dx)(4-x²)^½
½(4-x²)^(-½) (d/dx)(4-x²) (derivative of an expont)
½(4-x²)^(-½) [(d/dx) 4 - (d/dx)x²] (derivative of difference)
½(4-x²)^(-½) [0 - 2x] (derivative of constant and exponent)
½(4-x²)^(-½) (-2x) (algebra)
-x(4-x²)^(-½) (algebra)
-x/(4-x²)^½ (algebra)
1x/√(4-x²) (more algebra ☺) which is the final answer.
See why you needed to learn algebra? ☺
Doug
2006-10-31 22:42:43 · answer #1 · answered by doug_donaghue 7 · 1⤊ 0⤋
2
2006-11-01 06:37:10 · answer #2 · answered by pat 1 · 1⤊ 1⤋
Ignore the answers expect for doug. This must be done the way doug did the problem as it is a chain rule problem. So take the derivate he has and set it = to zero. Those will be your critical numbers that you are looking for. Sorry everyone else but most people did not realize that the equation looks like (4-x^2)^1/2 and you must use the chain rule
2006-11-01 07:41:49 · answer #3 · answered by Anonymous · 0⤊ 0⤋
+-2
2006-11-01 06:37:32 · answer #4 · answered by slimy dude 2 · 0⤊ 1⤋
The answer is easy! First, you look at the original function, and see if you can't simplify it a little.
(4*[X^2])^1/2 = 2X
Once you see how the root of two squared times X squared is simply two times X, you can use the very first rule for derivatives you ever learned, which is
if F=cx, F'=c
to find that the answer is 2.
2006-11-01 06:52:42 · answer #5 · answered by jtrench42 2 · 0⤊ 1⤋
the steps to the derivative are:
4-X^2
= (2)^2-(X)^2
= (2-X)(2+X) - Answer
2006-11-01 06:36:14 · answer #6 · answered by Enlightened 2 · 0⤊ 1⤋
And don't forget the negative square root.There are two answers.
2006-11-01 07:25:21 · answer #7 · answered by sydney m 2 · 0⤊ 1⤋
d/dx(sqrt(4-x^2))
=1/(2sqrt(4-x^2)) * (-2x)..chain rule
= -x/sqrt(4-x^2)
doug is right
i got the same nser too
2006-11-01 08:33:00 · answer #8 · answered by silent rain 2 · 0⤊ 0⤋
d/dx rt (4-x^2)
=1/2 (4-x^2)^3/2 (-2x)
=-x (4-x^2)^3/2
2006-11-01 06:52:07 · answer #9 · answered by . 3 · 0⤊ 1⤋