Using the definition of the derivative, find the derivative of g(t) = 1 / sqrt(t).

Using the definition of the derivative, find the derivative of g(t) = 1 / sqrt(t).

I started solving this one, and supposedly I'm incorrect so I won't bother typing out what I've gotten so far.

lim [(1 / sqrt(t + h)) - (1 / sqrt(t))] / h as h approaches 0.

^ I'm told to rationalize this bit first.

g'(t) = lim[h→0] (g(t+h) − g(t)) / h

g'(t) = lim[h→0] (1/√(t+h) − 1/√(t)) / h

g'(t) = lim[h→0] √(t+h)√(t) * (1/√(t+h) − 1/√(t)) / (h √(t+h)√(t))

g'(t) = lim[h→0] (√(t) − √(t+h)) / (h √(t+h)√(t))

g'(t) = lim[h→0] (√(t) − √(t+h)) (√(t) + √(t+h)) / (h √(t+h)√(t) (√(t) + √(t+h)))

g'(t) = lim[h→0] (t − (t+h) / (h √(t+h)√(t) (√(t) + √(t+h)))

g'(t) = lim[h→0] −h / (h √(t+h)√(t) (√(t) + √(t+h)))

g'(t) = lim[h→0] −1 / (√(t+h)√(t) (√(t) + √(t+h)))

g'(t) = −1 / (√(t)√(t) (√(t) + √(t)))

g'(t) = −1 / (t * 2√(t))

g'(t) = −1 / (2t^(3/2))