What is the derivative of $3x + 3lnx - 10^x(xlog_x10)$ ?

Question

$3x + 3lnx - 10^x(xlog_x10)$

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Answer 1 · 2018-07-04T14:20:32

$f'(x)=3+3/x-10^x*ln(10)(x/ln(x)*ln(10))-10^xln(10)*((ln(x)-1)/(ln(x))^2)$

We Need

$(ln(x))'=1/x$
and

$(10^x)'=10^x*ln(10)$
and the Quotient rule

$(u/v)'=(u'v-uv')/v^2$

and

$(x/ln(x))'=(ln(x)-x*1/x)/(ln(x))^2$
so we get

$f'(x)=3+3/x-10^xln(10)(x/ln(x)*ln(10))-10^x*ln(10)((ln(x)-1)/ln(x)^2)$