Thread: Find the slope of the tangent line

hi, I did something wrong but I do not what:
y = f(x)=1/sqrt(x) = x^-1/2

slope m= lim h->0 {f(x+h) - f(x)]/h

m=f'(x)= lim h->0 [1/sqrt(x+h) - 1/sqrt(x)]/h

then I multiply by [sqrt(x+h) + sqrt(x)] / [sqrt(x+h) + sqrt(x)]

m= lim h->0 {[x-(x+h)]/[sqrt(x+h)*sqrt(x)]} / h

m= lim h->0 h / [h*(sqrt(x+h)*sqrt(x)] = -1/2sqrt(x)

This is wrong, it must be -1/ 2sqrt(x^3)

Thanks for any help

Originally Posted by DBA

hi, I did something wrong but I do not what:
y = f(x)=1/sqrt(x) = x^-1/2

First principles is very messy here, using

Thank you for the reply, but I need to use the formula to solve the problem
slope m= lim h->0 [f(x+h) - f(x)]/h

for f(x) = 1/sqrt(x)

I know the answer, I just do not know how to get there with this formula.

Thanks