What is implicit 2x^3-e^{xy}=x*y^4 ?

The answer to implicit 2x^3-e^{xy}=x*y^4 is (dy)/(dx)=-(y^4-6x^2+e^{xy}y)/(x(e^{xy)+4y^3)}

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implicit 2x^3-e^{xy}=x*y^4

implicit derivative

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

\frac{d y}{d x} = - \frac{y ^{4} - 6 x ^{2} + e ^{x y} y}{x ( e ^{x y} + 4 y ^{3} )}

Solution steps

2 x^{3} - e^{x y} = x y^{4}

Treat

y

y (x)

Differentiate both sides:

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

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{y ^{4} - 6 x ^{2} + e ^{x y} y}{x ( e ^{x y} + 4 y ^{3} )}

\frac{d y}{d x} = - \frac{y ^{4} - 6 x ^{2} + e ^{x y} y}{x ( e ^{x y} + 4 y ^{3} )}

x \to 0 + lim (x^{9 x})

\frac{\partial}{\partial x} (5 x^{2})

\int \frac{x}{6 - x ^{2}} d x

x \to 3 lim (x^{2})

\int e^{x} y d x

What is implicit 2x^3-e^{xy}=x*y^4 ?
The answer to implicit 2x^3-e^{xy}=x*y^4 is (dy)/(dx)=-(y^4-6x^2+e^{xy}y)/(x(e^{xy)+4y^3)}