What is implicit (dy)/(dx),e^{xy}+x^2-y^2=12 ?

The answer to implicit (dy)/(dx),e^{xy}+x^2-y^2=12 is (dy)/(dx)=(-2x-e^{xy}y)/(e^{xy)x-2y}

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implicit (dy)/(dx),e^{xy}+x^2-y^2=12

implicit derivative

\frac{d y}{d x}, e^{x y} + x^{2} - y^{2} = 12

\frac{d y}{d x} = \frac{- 2 x - e ^{x y} y}{e ^{x y} x - 2 y}

Solution steps

e^{x y} + x^{2} - y^{2} = 12

Treat

y

y (x)

Differentiate both sides:

e^{x y} (y + x \frac{d y}{d x}) + 2 x - 2 y \frac{d y}{d x} = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- 2 x - e ^{x y} y}{e ^{x y} x - 2 y}

\frac{d y}{d x} = \frac{- 2 x - e ^{x y} y}{e ^{x y} x - 2 y}

What is implicit (dy)/(dx),e^{xy}+x^2-y^2=12 ?
The answer to implicit (dy)/(dx),e^{xy}+x^2-y^2=12 is (dy)/(dx)=(-2x-e^{xy}y)/(e^{xy)x-2y}