finding first derivative Find the first derivative for s ln

finding first derivative.

Find the first derivative for s = ln t/(1+ln t).

Solution

We\'ll differentiate the given function, with respect to t.

We\'ll use the quotient rule:

s\'(t) = [(ln t)\'*(1+ln t) - ln t*(1+ln t)\']/(1+ln t)^2

We\'ll differentiate and we\'ll get:

s\'(t) = [(1+ln t)/t - ln t/t]/(1+ln t)^2

s\'(t) = [(1+ln t - ln t)/t*(1+ln t)^2

We\'ll eliminate like terms from numerator:

s\'(t) = 1/t*(1+ln t)^2

The first derivative of s(t) = ln t/(1+ln t) is:

s\'(t) = 1/t*(1+ln t)^2