Need help with derivate of this function.
f(x) = 1/x, x can not be 0
lim (f(x+h)-f(x)) / h =
h->0
lim ((1/(x-h)) - (1/x)) / h =
h->0
lim (x-(x+h)) / (x(x+h)h) =
h->0
lim (-h) / (hx^2 + xh^2) =
h->0
Need help with this step
-1/x^2
Need help with derivate of this function.
f(x) = 1/x, x can not be 0
lim (f(x+h)-f(x)) / h =
h->0
lim ((1/(x-h)) - (1/x)) / h =
h->0
lim (x-(x+h)) / (x(x+h)h) =
h->0
lim (-h) / (hx^2 + xh^2) =
h->0
Need help with this step
-1/x^2
Factor out h from the denominator and cancel (it only approaches 0 so it can cancel)
Since we are taking the limit of h, not x it follows that . When this is put back into the original equation you get:
Which is what we'd expect knowing the power rule of differentiation.