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y=log[a^(4x).((x-5)/(x+4))^((3)/(4))]...

`y=log[a^(4x).((x-5)/(x+4))^((3)/(4))]`

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`y=log[a^(4x).((x-5)/(x+4))^((3)/(4))]`
`=loga^(4x)+log((x-5)/(x+4))^((3)/(4))`
`=4xloga+(3)/(4)log((x-5)/(x+4))`
`=4xloga+(3)/(4)[log(x-5)-log(x+4)]`
`therefore (dy)/(dx)=(d)/(dx)[4x loga+(3)/(4)log(x-5)-(3)/(4)log(x+4)]`
`=4loga(d)/(dx)(x)+(3)/(4)(d)/(dx)[log(x-5)]-(3)/(4)(d)/(dx)[log(x+4)]`
`=4logaxx1+(3)/(4)xx(1)/(x-5).(d)/(dx)(x-5)-(3)/(4)xx(1)/(x+4).(d)/(dx)(x+4)`
`=4loga+(3)/(4(x-5)).(1-0)-(3)/(4(x+4)).(1+0)`
`=4loga+(3)/(4(x-5))-(3)/(4(x+4))`
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