What is implicit (dy)/(dx),xy^3+10y^{11}=9 ?

The answer to implicit (dy)/(dx),xy^3+10y^{11}=9 is (dy)/(dx)=-y/(3x+110y^8)

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implicit (dy)/(dx),xy^3+10y^{11}=9

implicit derivative

\frac{d y}{d x}, x y^{3} + 10 y^{11} = 9

\frac{d y}{d x} = - \frac{y}{3 x + 110 y ^{8}}

Solution steps

x y^{3} + 10 y^{11} = 9

Treat

y

y (x)

Differentiate both sides:

y^{3} + 3 x y^{2} \frac{d y}{d x} + 110 y^{10} \frac{d y}{d x} = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{y}{3 x + 110 y ^{8}}

\frac{d y}{d x} = - \frac{y}{3 x + 110 y ^{8}}

What is implicit (dy)/(dx),xy^3+10y^{11}=9 ?
The answer to implicit (dy)/(dx),xy^3+10y^{11}=9 is (dy)/(dx)=-y/(3x+110y^8)