What is implicit (dy)/(dx),x^2e^y-y^4=e^x ?

The answer to implicit (dy)/(dx),x^2e^y-y^4=e^x is (dy)/(dx)=(e^x-2e^yx)/(e^yx^2-4y^3)

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implicit (dy)/(dx),x^2e^y-y^4=e^x

implicit derivative

\frac{d y}{d x}, x^{2} e^{y} - y^{4} = e^{x}

\frac{d y}{d x} = \frac{e ^{x} - 2 e ^{y} x}{e ^{y} x ^{2} - 4 y ^{3}}

Solution steps

x^{2} e^{y} - y^{4} = e^{x}

Treat

y

y (x)

Differentiate both sides:

2 x e^{y} + e^{y} \frac{d y}{d x} x^{2} - 4 y^{3} \frac{d y}{d x} = e^{x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{e ^{x} - 2 e ^{y} x}{e ^{y} x ^{2} - 4 y ^{3}}

\frac{d y}{d x} = \frac{e ^{x} - 2 e ^{y} x}{e ^{y} x ^{2} - 4 y ^{3}}

What is implicit (dy)/(dx),x^2e^y-y^4=e^x ?
The answer to implicit (dy)/(dx),x^2e^y-y^4=e^x is (dy)/(dx)=(e^x-2e^yx)/(e^yx^2-4y^3)