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

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

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

implicit derivative

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

\frac{d y}{d x} = \frac{1}{3 y ^{2} + 1}

Solution steps

y^{3} + y = x

Treat

y

y (x)

Differentiate both sides:

3 y^{2} \frac{d y}{d x} + \frac{d y}{d x} = 1

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{1}{3 y ^{2} + 1}

\frac{d y}{d x} = \frac{1}{3 y ^{2} + 1}

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