Question

How do you find the implicit differentiation of `xe^y+ye^x=1`?

Answer 1

`dy/dx=-(e^y+ye^x)/(xe^y+e^x)`

Explanation:

differentiate `color(blue)"implicitly with respect to x"`

Both terms on the left have to be differentiated using the `color(blue)"product rule"`

`rArr(xe^y.dy/dx+e^y.1)+(ye^x+e^x.dy/dx)=0`

`rArrdy/dx(xe^y+e^x)=-e^y-ye^x`

`rArrdy/dx=-(e^y+ye^x)/(xe^y+e^x)`