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Find the derivative of `h(x)=ln10x+log_4 10x` 

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lfryerda eNotes educator | Certified Educator

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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}` .

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islnds | Student

Its not suppose to be 410 in the question. The 4 is suppose the be a subscript. It was typed that way initially, but somehow when the question got finalized it became 410.

button33 | Student

h'(x)=(1/x)+(1/x ln4)