Question

how do you find the derivative of f(x)=square root of (x-1)?

Answer 1

express it in exponential form first
(x-1)^1/2

now use power rule
1/2(x-1)^-1/2

d/dx = 1/2sqrt(x-1)

Answer 2

you should perhaps memorize the derivative of
\[\sqrt{x}\] because it comes up all the time.
it is
\[\frac{1}{2\sqrt{x}}\] you can get it using the "power rule" but it is always the same so easier just to know it.
kind of like knowing that 8 times 7 is 56

Answer 3

so when you take out the square root to 1/2 you don't multiply that with the x and -1 inside the parenthesis? only the outside of them, oh i see

Answer 4

so
\[\frac{d}{dx}\sqrt{x-1}=\frac{1}{2\sqrt{x-1}}\] and be done

Answer 5

oh okay now i can substitute x value into it to find the slope. and therefore get my equation.