Question

How can I find dy/dx for the equation e^(xy)+xy=1

Answer 1

implicit differentiation
take derivative of every term, if it is a "y" term multiply derivative by dy/dx

Answer 2

for "xy" use product rule
\[\rightarrow (1)y + x(1)\frac{dy}{dx}\]

Answer 3

That makes sense! Does the e^(xy) get cancelled out? If I don't include that part, my answer matches up with what is in my book. Otherwise, I don't know what to do with it.

Answer 4

no derivative of e^u = e^u

Answer 5

\[(y+x \frac{dy}{dx}) e^{xy} +y+x \frac{dy}{dx} = 0\]
isolate dy/dx