derivitives?

Question

How do you calculate the derivitive of the equation
sqrt( 1-x^2)

Answer 1

set all square roots when taking the derivative like this
(1-x^2)^(1/2)
having it to the (1/2) power
using that you'll get:
(1/2)(1-x^2)^(-1/2)*2x
sooo it'll come out to
2x/(2sqrt(1-x^2))
simplified you get
x/(sqrt(1-x^2)

Answer 2

You use the chain rule. If you have a function f(g(x)), then the derivative is f'(g(x))*g'(x).


In this case, sqrt(x) is f(x), and 1-x^2 is g(x). Make sure that that makes sense.

Rewrite the equation as : (1-x^2)^(1/2), which is simply the square root in exponent form. Then differentiate:

(1/2)(1-x^2)^(-1/2) is f'(g(x)) by the power rule, then g'(x) = -2x.

So the derivative is -x/(sqrt(1-x^2))


Edit: Priyanka, you forget to subtract 1 from the exponent, 1/2. This leaves an exponent of -1/2. So your answer is wrong.

Answer 3

the easiest way is to first rewrite it so that it is

(1-x^2)^1/2

now use the power rule

= 1/2 * (1 -x^2)(-2x)

simplify

= x^2 - 1

Answer 4

y = sqrt (1 - x^2) = (1 - x^2)^(1/2)
y' = [(1/2)(1 - x^2)^-(1/2)](-2x)
y' = -x(1 - x^2)^-(1/2) = -x/sqrt (1 - x^2)