# Thread: why is the derivative of the square root of (1-x) negative?

1. ## why is the derivative of the square root of (1-x) negative?

I get the derivative of the sqrt(x) as 1/(2*sqrt(x)) but for x= 1-x the derivative is -1/(2*sqrt(x)) .

Is this because we have multiplied by the derivative of (1-x) which would be -1?

thanks!

2. ## Re: why is the derivative of the square root of (1-x) negative?

Originally Posted by kingsolomonsgrave
I get the derivative of the sqrt(x) as 1/(2*sqrt(x)) but for x= 1-x the derivative is -1/(2*sqrt(x)) .

Is this because we have multiplied by the derivative of (1-x) which would be -1?

thanks!
First, check the domains of your functions and their derivatives. Second, note that sqrt{1 - x} is monotonically decreasing. How would you interpret the slope of a monotonically decreasing function?

-Dan