What is implicit (dy)/(dx),(4x+4y)3=64x^3+64y^3 ?

The answer to implicit (dy)/(dx),(4x+4y)3=64x^3+64y^3 is (dy)/(dx)=(16x^2-1)/(1-16y^2)

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implicit (dy)/(dx),(4x+4y)3=64x^3+64y^3

implicit derivative

\frac{d y}{d x}, (4 x + 4 y) 3 = 64 x^{3} + 64 y^{3}

\frac{d y}{d x} = \frac{16 x ^{2} - 1}{1 - 16 y ^{2}}

Solution steps

(4 x + 4 y) \cdot 3 = 64 x^{3} + 64 y^{3}

Treat

y

y (x)

Differentiate both sides:

3 (4 + 4 \frac{d y}{d x}) = 192 x^{2} + 192 y^{2} \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{16 x ^{2} - 1}{1 - 16 y ^{2}}

\frac{d y}{d x} = \frac{16 x ^{2} - 1}{1 - 16 y ^{2}}

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\int \frac{1}{2 + 3 x - 2 x ^{2}} d x

\frac{d y}{d x} = \frac{( x - y )}{x}

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\frac{d}{d x} (2 y - \frac{1}{x} + cos (3 x))

What is implicit (dy)/(dx),(4x+4y)3=64x^3+64y^3 ?
The answer to implicit (dy)/(dx),(4x+4y)3=64x^3+64y^3 is (dy)/(dx)=(16x^2-1)/(1-16y^2)