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

1 Answer
Sharkbasket
Mar 25, 2018

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

Explanation:

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

Using implicit differentiation:

#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)#

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