What is implicit x^5+x^2y+9y^2=13 ?

The answer to implicit x^5+x^2y+9y^2=13 is (dy)/(dx)=(-5x^4-2xy)/(x^2+18y)

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implicit x^5+x^2y+9y^2=13

implicit derivative

x^{5} + x^{2} y + 9 y^{2} = 13

\frac{d y}{d x} = \frac{- 5 x ^{4} - 2 x y}{x ^{2} + 18 y}

Solution steps

x^{5} + x^{2} y + 9 y^{2} = 13

Treat

y

y (x)

Differentiate both sides:

5 x^{4} + 2 x y + \frac{d y}{d x} x^{2} + 18 y \frac{d y}{d x} = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- 5 x ^{4} - 2 x y}{x ^{2} + 18 y}

\frac{d y}{d x} = \frac{- 5 x ^{4} - 2 x y}{x ^{2} + 18 y}

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

\frac{\partial}{\partial x} (cos (3 x))

\int (sec (x) - \frac{1}{sin ( x )} + cos (x)) d x

\frac{\partial}{\partial x} (sin (\frac{x}{1 + y}))

What is implicit x^5+x^2y+9y^2=13 ?
The answer to implicit x^5+x^2y+9y^2=13 is (dy)/(dx)=(-5x^4-2xy)/(x^2+18y)