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If f' (x) = sin (log x) and y = f((2...

If ` f' (x) = sin (log x)` and `y = f((2x+3)/(3- 2x)), " then " (dy)/(dx) " at " x = 1 ` is equal to

A

` 6 sin log (5)`

B

`5 sin log (6)`

C

`12 sin log (5)`

D

`5 sin log (12)`

Text Solution

Verified by Experts

The correct Answer is:
C
`(dy)/(dx) = f'((2x +3)/(3 - 2x)) (d)/(dx) ((2x + 3)/(3-2x)) `
` = sin [log((2 x +3)/(3 - 2x))][((3-2x)(2)- (2x + 3)(-2))/(3-2x)^(2)]`
`= (12)/((3 - 2x)^(2) )""sin[ log ((2x+3)/(3 -2x)]`
`rArr ((dy)/(dx))_(x=1) = (12)/((3-2)^(2) )"" sin log (5) = 12 sin log 5 `.
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