Calculus Help
posted by Mello .
Use f(x)= 1/(square root(x)+1) to answer the following;
 Use the difference quotient f'(x)=lim z>x (f(x)f(z))/ (xz) to find f'(x)!
Please show steps!!!
Thank you!!!

f(x) = 1/[ x^.5 +1 ]
f(z) = 1/[ z^.5 + 1 }
f(x)f(z) = 1/[ x^.5 +1 ]  1/[ z^.5 + 1]
= ([z^.5+1][x^.5+1])/(x^.5z^.5 +x^.5+z^.5+1)
= (z^.5x^.5) /(x^.5z^.5 +x^.5+z^.5+1)
Divide by (xz) which is (x^.5z^.5)(x^.5+z^.5)
and get
(x^.5+z^.5) / (x^.5z^.5 +x^.5+z^.5+1)
let z >x
 2 x^.5 / (x +2 sqrt x + 1)
check my arithmetic !!!
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