How do you find the derivative of # x ln y - y ln x = 1#?

1 Answer
Jim G.
Jun 27, 2017

#dy/dx=(y/x-lny)/(x/y-lnx)#

Explanation:

#"using "color(blue)"implicit differentiation"#

#"differentiate " xlny" and " ylnx" using the"#
#color(blue)"product rule"#

#(x. 1/y . dy/dx+lny)-(y. 1/x+lnx. dy/dx)=0#

#rArrx/ydy/dx+lny-y/x-lnxdy/dx=0#

#rArrdy/dx(x/y-lnx)=y/x-lny#

#rArrdy/dx=(y/x-lny)/(x/y-lnx)#

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