How to differentiate e^(xy)+1/y=5x+6?

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Answer 1 · 2018-03-25T19:46:38

$dy/dx=(5-ye^(xy))/(xe^(xy)-1/y^2)$

$e^(xy)+y^-1=5x+6$

$e^(xy)*d/dx(xy) -y^-2*d/dx(y)=5$

$e^(xy)(y+xdy/dx)-y^-2dy/dx=5$

$ye^(xy)+xe^(xy)dy/dx-y^-2dy/dx=5$

$dy/dx(xe^(xy)-y^-2)=5-ye^(xy)$

$dy/dx=(5-ye^(xy))/(xe^(xy)-1/y^2)$