If f(x) = log{u(x)/v{x}}, u(1) and u'(1) = v'(1) = 2, then find the value of f'(1).

Question

If f(x) = log\(\Big\{\cfrac{u(\text x)}{v(\text x)}\Big\},\) u(1) = v (1) and u'(1) = v'(1) = 2, then find the value of f'(1).

Answer 1

Using the Chain Rule of Differentiation,

Since, u(1) = v(1),

2v(1) – 2u(1) = 0

i.e., f’(1) = 0