What is implicit x^5+x^2y^3=0 ?

The answer to implicit x^5+x^2y^3=0 is (dy)/(dx)=-(5x^3+2y^3)/(3xy^2)

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implicit x^5+x^2y^3=0

implicit derivative

x^{5} + x^{2} y^{3} = 0

\frac{d y}{d x} = - \frac{5 x ^{3} + 2 y ^{3}}{3 x y ^{2}}

Solution steps

x^{5} + x^{2} y^{3} = 0

Treat

y

y (x)

Differentiate both sides:

5 x^{4} + 2 x y^{3} + 3 y^{2} \frac{d y}{d x} x^{2} = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{5 x ^{3} + 2 y ^{3}}{3 x y ^{2}}

\frac{d y}{d x} = - \frac{5 x ^{3} + 2 y ^{3}}{3 x y ^{2}}

\int \frac{( ln ( x ^{7} ) )}{x} d x

y^{^{'}} = \frac{3 x ^{2} - e ^{x}}{2 y - 5}

\frac{\partial}{\partial x} (x^{2} + y^{2} + 1)

y = 4 ln (cos (x))

\int \frac{x ^{2} - 4}{x ^{4}} d x

What is implicit x^5+x^2y^3=0 ?
The answer to implicit x^5+x^2y^3=0 is (dy)/(dx)=-(5x^3+2y^3)/(3xy^2)