Solve 6x-y^3=0 - ScanMath

Solve the equation

Solve for x

Solve for y

x = \frac{y ^{3}}{6}

Show Solution

Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Symmetry with respect to the origin

Show Solution

r = 0 r = 6 cos (θ) csc (θ) \times ∣ csc (θ) ∣ r = - 6 cos (θ) csc (θ) \times ∣ csc (θ) ∣

Show Solution

Find the derivative with respect to x

Find the derivative with respect to y

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

Show Solution

Find the second derivative with respect to x

Find the second derivative with respect to y

\frac{d ^{2} y}{d x ^{2}} = - \frac{8}{y ^{5}}

Calculate

6 x - y^{3} = 0

Take the derivative of both sides

\frac{d}{d x} (6 x - y^{3}) = \frac{d}{d x} (0)

Calculate the derivative

More Steps

6 - 3 y^{2} \frac{d y}{d x} = \frac{d}{d x} (0)

Calculate the derivative

6 - 3 y^{2} \frac{d y}{d x} = 0

Move the constant to the right-hand side and change its sign

- 3 y^{2} \frac{d y}{d x} = 0 - 6

Removing 0 doesn't change the value,so remove it from the expression

- 3 y^{2} \frac{d y}{d x} = - 6

Divide both sides

\frac{- 3 y ^{2} \frac{d y}{d x}}{- 3 y ^{2}} = \frac{- 6}{- 3 y ^{2}}

Divide the numbers

\frac{d y}{d x} = \frac{- 6}{- 3 y ^{2}}

Cancel out the common factor - 3

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

Take the derivative of both sides

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

Calculate the derivative

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

Use differentiation rules

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

Rewrite the expression in exponential form

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

Calculate the derivative

More Steps

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

Rewrite the expression

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

Calculate

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

Use equation \frac{d y}{d x} = \frac{2}{y ^{2}} to substitute

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

Solution

More Steps

\frac{d ^{2} y}{d x ^{2}} = - \frac{8}{y ^{5}}

Show Solution