What is implicit e^{x^2y}=x+y ?

The answer to implicit e^{x^2y}=x+y is (dy)/(dx)=(1-2e^{x^2y}xy)/(e^{x^2y)x^2-1}

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implicit e^{x^2y}=x+y

implicit derivative

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

\frac{d y}{d x} = \frac{1 - 2 e ^{x^{2} y} x y}{e ^{x^{2} y} x ^{2} - 1}

Solution steps

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

Treat

y

y (x)

Differentiate both sides:

e^{x^{2} y} (2 x y + \frac{d y}{d x} x^{2}) = 1 + \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{1 - 2 e ^{x^{2} y} x y}{e ^{x^{2} y} x ^{2} - 1}

\frac{d y}{d x} = \frac{1 - 2 e ^{x^{2} y} x y}{e ^{x^{2} y} x ^{2} - 1}

\frac{\partial}{\partial x} (\frac{x}{x ^{2} - y ^{2}})

\frac{d}{d x} (- \frac{8}{1 - 8 x})

(2 - x^{2})^{\frac{1}{2}}

\int_{0}^{1} \frac{1}{x + 1} d x

\int_{0}^{1} (x + x) d x

What is implicit e^{x^2y}=x+y ?
The answer to implicit e^{x^2y}=x+y is (dy)/(dx)=(1-2e^{x^2y}xy)/(e^{x^2y)x^2-1}