Thread: Proving the quotient rule using this definition of differentiability

1. Proving the quotient rule using this definition of differentiability

Hi,
I've been working on this problem for an hour and I don't know what I'm doing wrong where I can't solve it. Help would be very much appreciated.

First I'm using this definition of differentiability:

f is differentiable at a if:
f(a+h) = f(a) + f'(a)h + E(h) where E(h)/h --> 0 as h-->0

Now, I'm trying to show:
If g(x) = 1/f(x) and f(a)=/=0 then we have: g'(a) = -f'(a)/[f(a)^2]

Thanks guy

2. Originally Posted by AKTilted
Hi,
I've been working on this problem for an hour and I don't know what I'm doing wrong where I can't solve it. Help would be very much appreciated.

First I'm using this definition of differentiability:

f is differentiable at a if:
f(a+h) = f(a) + f'(a)h + E(h) where E(h)/h --> 0 as h-->0

What is f, anyway? And how's f'(a) defined in your book?

Tonio

Now, I'm trying to show:
If g(x) = 1/f(x) and f(a)=/=0 then we have: g'(a) = -f'(a)/[f(a)^2]

Thanks guy
.