Solve x^2 ( y - 3\sqrt 2x ) 2 = 1

Question

Solve the equation

y = \frac{1 + 6 x ^{2} 2 x}{2 x ^{2}}

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Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Not symmetry with respect to the origin

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Find the derivative with respect to x

Find the derivative with respect to y

\frac{d y}{d x} = \frac{- 2 2 \times y + 15 x}{2 \times x}

Calculate

x^{2} (y - 3 2 x) 2 = 1

Simplify the expression

2 x^{2} y - 6 x^{2} 2 x = 1

Take the derivative of both sides

\frac{d}{d x} (2 x^{2} y - 6 x^{2} 2 x) = \frac{d}{d x} (1)

Calculate the derivative

More Steps

\frac{4 x y 2 x + 2 x ^{2} \frac{d y}{d x} \times 2 x - 30 x ^{2}}{2 x} = \frac{d}{d x} (1)

Calculate the derivative

\frac{4 x y 2 x + 2 x ^{2} \frac{d y}{d x} \times 2 x - 30 x ^{2}}{2 x} = 0

Rewrite the expression

\frac{4 x y 2 x - 30 x ^{2} + 2 x ^{2} 2 x \times \frac{d y}{d x}}{2 x} = 0

Simplify

4 x y 2 x - 30 x^{2} + 2 x^{2} 2 x \times \frac{d y}{d x} = 0

Move the constant to the right side

2 x^{2} 2 x \times \frac{d y}{d x} = 0 - (4 x y 2 x - 30 x^{2})

Subtract the terms

More Steps

2 x^{2} 2 x \times \frac{d y}{d x} = - 4 x y 2 x + 30 x^{2}

Divide both sides

\frac{2 x ^{2} 2 x \times \frac{d y}{d x}}{2 x ^{2} 2 x} = \frac{- 4 x y 2 x + 30 x ^{2}}{2 x ^{2} 2 x}

Divide the numbers

\frac{d y}{d x} = \frac{- 4 x y 2 x + 30 x ^{2}}{2 x ^{2} 2 x}

Divide the numbers

More Steps

\frac{d y}{d x} = \frac{- 2 y 2 x + 15 x}{x 2 x}

Solution

More Steps

\frac{d y}{d x} = \frac{- 2 2 \times y + 15 x}{2 \times x}

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