What is the differential wrt x of 3^x lnx ?

1 Answer
Jim G.
Feb 18, 2018

#3^x(ln3x+1/x)#

Explanation:

#"differentiate using the "color(blue)"product rule"#

#"given "y=f(x)g(x)" then"#

#dy/dx=f(x)g'(x)+g(x)f'(x)larrcolor(blue)"product rule"#

#f(x)=3^xrArrf'(x)=3^xln3#

#g(x)=lnxrArrg'(x)=1/x#

#rArrd/dx(3^xlnx)#

#=3^x/x+3^xln3lnx#

#=3^x(ln3x+1/x)#

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