If f x = 2 + x 1 + x 1 + x , then f ′ 0 is equal to

Question

If f x = 2 + x 1 + x 1 + x , then f ′ 0 is equal to, 2 log 2, log 2, 3 log 2 − 1, 2 log 2 − 1

MARKS App · Accepted Answer

By taking logarithm on both sides, log f ( x ) = ( 1 + x ) log ( 2 + x ) − log ( 1 + x ) On differentiating, we get, 1 f x · f ' x = 1 + x 2 + x + log ( 2 + x ) − 1 + x 1 + x − log ( 1 + x ) Now, put x = 0 f ' ( 0) = f 0 1 + log 2 2 − 1 = f 0 log 2 − 1 2 = 2 log 2 − 1 ∵ f 0 = 2

Search any question & find its solution

Looking for more such questions to practice?