Calculus
posted by Tori on .
Find the derivative of the function using the definition of a derivative.
F(x)=squareroot(13x)
Please show work for understanding, thank you! :)

recall that (a+b)^n = a^n + na^(n1)*b + n(n1)/2 a^(n2)*b^2 + ...
So,
(13(x+h))^1/2 = ((13x)  3h)^1/2
= (13x)^1/2 + (1/2)(13x^(1/2)*(3h) + (*)(3h)^2 + ...
f(x+h)  f(x) =
(13x)^1/2 + (1/2)(13x^(1/2)*(3h) + (*)(3h)^2 + ...  (13x)^1/2
= (1/2)(13x^(1/2)*(3h) + (*)(3h)^2 + ...
now divide that by h to get
(1/2)(13x^(1/2)*(3) + (*)(9h) + ...
Now take the limit as h>0.
The (9h) term and all the other higherpowerofh terms vanish, leaving
3/2 (13x)^(1/2)