To find the derivative of this function, we need to change the base of the second term into base e, and then apply normal derivative rules.

`h(x)=ln 10x+log_4 10x` change base of second term

`=ln 10x+{ln 10x}/{ln4}` now expand both terms using multiplcation rule

`=ln 10+ln x+ln10/ln4+lnx/ln4` now differentiate

`h'(x)=0+1/x+0+1/{xln4}`

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To find the derivative of this function, we need to change the base of the second term into base e, and then apply normal derivative rules.

`h(x)=ln 10x+log_4 10x` change base of second term

`=ln 10x+{ln 10x}/{ln4}` now expand both terms using multiplcation rule

`=ln 10+ln x+ln10/ln4+lnx/ln4` now differentiate

`h'(x)=0+1/x+0+1/{xln4}`

**The derivative is `h'(x)=1/x+1/{xln4}` .**