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)#