Question

Suppose x^6 e^−2y = ln (xy).
Find dy/dx by implicit differentiation.

Answer 1

\[x^6e^{-2y}=ln(xy)\]

Answer 2

Differentiate both sides, we get
\[6x^5e^{-2y}+x^6(-2e^{-2y})\frac{dy}{dx}=\frac1x+\frac1y\frac{dy}{dx}\]

Answer 3

so dy/dx= \[(\frac{ 1 }{ x }-6x^5e ^{-2y})/(-\frac{ 1 }{ y }+(x^6(-2e^{-2y})))\]

Answer 4

yes