How do you implicitly differentiate #y= y^2 + e^(x y) #?
1 Answer
Dec 1, 2016
We use the power rule and the rule if
Hence:
#1(dy/dx) = 2y(dy/dx) + (y + x(dy/dx))e^(xy)#
Solving for
#dy/dx = 2y(dy/dx) + ye^(xy) + x(dy/dx)e^(xy)#
#dy/dx - 2y(dy/dx) - xe^(xy)(dy/dx) = ye^(xy)#
#dy/dx(1 - 2y - xe^(xy)) = ye^(xy)#
#dy/dx = (ye^(xy))/(1 - 2y - xe^(xy))#
Hopefully this helps!
