यदि `y=log_(10)x+log_(x) 10 +log_(x)x+log_(10)10` है, तब `(dy)/(dx)` बराबर है

Options

A. `(1)/(x log_(e )10)-(log_(e )10)/(x(log_(e )x)^(2))`
B. `(1)/(x log_(e )10) -(1)/(x log_(10)e)`
C. `(1)/(x log_(e )10) -(log_(e )10)/(x ( log_(e )x))`
D. इनमें से कोई नहीं

Answer

A

Explanation

`y`` =log_(10)x +log_(x) 10 ``+log_(x) x +log_(10)10`

चूंकि `log_ba=(log_ea)/(log_eb)`

`y` `=(log_ex)/(log_e10) ``+(log_(e) 10)/(log_(e )x)``+(log_(e) x)/(log_(e )x)``+(log_(e) 10)/(log_(e )10)`

`y` `=(log_ex)/(log_e10)`` +(log_(e) 10)/(log_(e )x)``+1+1`

`[(dlogx)/(dx)``=1/x]`

`(dy)/(dx)``=(1)/(xlog_(e)10)`` +(log_ex xx 0-(log_(e )10))/(x(log_(e )x)^(2))``+0+0`

`(dy)/(dx)``=(1)/(x log_(e )10)``-(log_(e )10)/(x(log_(e )x)^(2))`