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}}

f (x) = 2 sin^{3} (x)

\int \frac{- 4 x ^{5} - x ^{\frac{3}{4}} - 2}{9 x ^{\frac{4}{3}}} d x

\int 2 x (x^{2} + 7)^{8} d x

\int x (x^{3} - 2 x^{2}) d x

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

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)