Question

the value of f'(l) if m( l)= n( l)=l and m'(l)=n'(l)=2 and where f(x) =log [m(x)/n(x)]​

Answer 1

Given :    f(x) =log [m(x)/n(x)]​  m( l)= n( l)=l and m'(l)=n'(l)=2

To find : value of f'(l)

Solution:

f(x) = log [m(x)/n(x)]​

f'(x) = (1/ [m(x)/n(x)]​ )  d (m(x)/(n(x)) /dx

=> f'(x) =  ( n(x) / m(x) ) {  m(x) (-n'(x)/((n(x))²)    + m'(x)/(n(x)) }

=> f'(x) =    ( n(x) / m(x) )  (  ( -m(x)n'(x)  + m'(x)n(x) ) / (n(x))²

=> f'(x) =  ( 1/(m(x)n(x) ) (  m'(x)n(x) - m(x)n'(x)  )

f'(l) =  ( 1/(m(l)n(l) ) (  m'(l)n(l) - m(l)n'(l)  )

=>  f'(l) =  (1/(l)(l)) ( 2l - 2l)

=>  f'(l) =   0

f'(l) =   0

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