1.

If `y=log_(10)x+log_(x)10+log_(x)x+log_(10)10` then what is `((dy)/(dx))_(x=10)` equal to?A. 10B. 2C. 1D. 0

Answer» Correct Answer - D
`y = log_(10) x + log_(x) x + log_(10)10`
`y=log_(10)x+log_(x)10 + 1 + 1`
Differentiating equation w.r.t. x
`(dy)/(dx)=(1)/(xlog_(e)10)-(1)/((log_(10)x)^(2)).(1)/((x log 10))`
`=(1)/(xlog_(e)10)[1-(1)/((log_(10)x)^(2))]`
`((dy)/(dx))_(x=10) =(1)/(10 log_(e)10)[1-1]=0`
`[{:("Note:" log_(x)10=(log_(10)10)/(log_(10)x)=(1)/(log_(10)x)),((d)/(dx)[(1)/(log_(1)x)]=-(l0g_(10)x)^(-2)xx(1)/(x log_(e)10)),(" "=-(1)/((log_(10)x)^(2)xlog_(e)10)):}]`


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