Bonjour ;
1.
On a : f(a + h) - f(a) = 1/v(a + h) - 1/v(a)
= (v(a) - v(a + h))/(v(a)v(a + h)) = - (v(a + h) - v(a))/(v(a)v(a + h)) .
tau(h) = (f(a + h) - f(a))/h = - (v(a + h) - v(a))/(h v(a)v(a + h))
= - 1/(v(a)v(a + h)) x (v(a + h) - v(a))/h .
2.
lim(h --> 0) 1/(v(a)v(a + h)) = 1/v²(a) .
lim(h --> 0) (v(a + h) - v(a))/h = v ' (a) .
3.
lim(h --> 0) tau(h) = lim(h --> 0) - 1/(v(a)v(a + h)) x (v(a + h) - v(a))/h
= - 1/v²(a) x v ' (a) = - (v ' (a))/v²(a) .
f ' (a) = lim(h --> 0) tau(h) = - (v ' (a))/v²(a) .
