How do you differentiate e^x /lnxexlnx?

1 Answer
Jim G.
May 9, 2018

(e^x(lnx-1/x))/(lnx)^2ex(lnx−1x)(lnx)2

Explanation:

"differentiate using the "color(blue)"quotient rule"differentiate using the quotient rule

"given "y=(g(x))/(h(x))" then"given y=g(x)h(x) then

dy/dx=(h(x)g'(x)-g(x)h'(x))/(h(x))^2larrcolor(blue)"quotient rule"

g(x)=e^xrArrg'(x)=e^x

h(x)=lnxrArrh'(x)=1/x

rArrd/dx((e^x)/(lnx))

=(e^xlnx-1/x e^x)/(lnx)^2=(e^x(lnx-1/x))/(lnx)^2

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