What is implicit (dy)/(dx),x^3y^5+3x=8y^3+1 ?

The answer to implicit (dy)/(dx),x^3y^5+3x=8y^3+1 is (dy)/(dx)=(-3x^2y^5-3)/(y^2(-24+5x^3y^2))

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implicit (dy)/(dx),x^3y^5+3x=8y^3+1

implicit derivative

\frac{d y}{d x}, x^{3} y^{5} + 3 x = 8 y^{3} + 1

\frac{d y}{d x} = \frac{- 3 x ^{2} y ^{5} - 3}{y ^{2} ( - 24 + 5 x ^{3} y ^{2} )}

Solution steps

x^{3} y^{5} + 3 x = 8 y^{3} + 1

Treat

y

y (x)

Differentiate both sides:

3 x^{2} y^{5} + 5 y^{4} \frac{d y}{d x} x^{3} + 3 = 24 y^{2} \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- 3 x ^{2} y ^{5} - 3}{y ^{2} ( - 24 + 5 x ^{3} y ^{2} )}

\frac{d y}{d x} = \frac{- 3 x ^{2} y ^{5} - 3}{y ^{2} ( - 24 + 5 x ^{3} y ^{2} )}

What is implicit (dy)/(dx),x^3y^5+3x=8y^3+1 ?
The answer to implicit (dy)/(dx),x^3y^5+3x=8y^3+1 is (dy)/(dx)=(-3x^2y^5-3)/(y^2(-24+5x^3y^2))