What is implicit (dy)/(dx),x^5y+5xy^5=x+y ?

The answer to implicit (dy)/(dx),x^5y+5xy^5=x+y is (dy)/(dx)=(1-5x^4y-5y^5)/(x^5+25xy^4-1)

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implicit (dy)/(dx),x^5y+5xy^5=x+y

implicit derivative

\frac{d y}{d x}, x^{5} y + 5 x y^{5} = x + y

\frac{d y}{d x} = \frac{1 - 5 x ^{4} y - 5 y ^{5}}{x ^{5} + 25 x y ^{4} - 1}

Solution steps

x^{5} y + 5 x y^{5} = x + y

Treat

y

y (x)

Differentiate both sides:

5 x^{4} y + \frac{d y}{d x} x^{5} + 5 (y^{5} + 5 x y^{4} \frac{d y}{d x}) = 1 + \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{1 - 5 x ^{4} y - 5 y ^{5}}{x ^{5} + 25 x y ^{4} - 1}

\frac{d y}{d x} = \frac{1 - 5 x ^{4} y - 5 y ^{5}}{x ^{5} + 25 x y ^{4} - 1}

x \to 2 + lim (cos (x - 2))

\int y e^{y^{2}} d y

x y^{^{'}} - 2 y = x^{2}

\int_{0}^{3} \frac{1}{( 1 - x ) ^{2}} d x

\frac{x}{4 x + 9}

What is implicit (dy)/(dx),x^5y+5xy^5=x+y ?
The answer to implicit (dy)/(dx),x^5y+5xy^5=x+y is (dy)/(dx)=(1-5x^4y-5y^5)/(x^5+25xy^4-1)