Question

How do you implicitly differentiate `9=e^y/e^x+y^3-xy`?

Answer 1

`d/dx(e^y/e^x +y^3-xy=9)`
`0=-e^y/e^x+e^y/e^x dy/dx+3y^2dy/dx-xdy/dx-y`
`dy/dx=(e^y/e^x+y)/(e^y/e^x+3y^2-x`

Explanation:

Take the derivative of both sides but remember to put dy/dx or y' next the derivative of the y term. Then put all the terms with dy/dx in it on one side and everything else on the other side and solve for dy/dx.