What is implicit (dy)/(dx),x^3+y^3=4xy+1 ?

The answer to implicit (dy)/(dx),x^3+y^3=4xy+1 is (dy)/(dx)=(4y-3x^2)/(3y^2-4x)

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implicit (dy)/(dx),x^3+y^3=4xy+1

implicit derivative

\frac{d y}{d x}, x^{3} + y^{3} = 4 x y + 1

\frac{d y}{d x} = \frac{4 y - 3 x ^{2}}{3 y ^{2} - 4 x}

Solution steps

x^{3} + y^{3} = 4 x y + 1

Treat

y

y (x)

Differentiate both sides:

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

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{4 y - 3 x ^{2}}{3 y ^{2} - 4 x}

\frac{d y}{d x} = \frac{4 y - 3 x ^{2}}{3 y ^{2} - 4 x}

What is implicit (dy)/(dx),x^3+y^3=4xy+1 ?
The answer to implicit (dy)/(dx),x^3+y^3=4xy+1 is (dy)/(dx)=(4y-3x^2)/(3y^2-4x)