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

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

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

implicit derivative

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

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

Solution steps

y^{3} = x^{4}

Treat

y

y (x)

Differentiate both sides:

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

Isolate

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

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

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