If -2y^(3)-x^(3)=5xy then find (dy)/(dx) in terms of x and y. Answer: (dy)/(dx)=

Differentiate Left Side: We are given the equation -2y^(3) - x^(3) = 5xy. To find (dy)/(dx), we need to differentiate both sides of the equation with respect to x, using implicit differentiation.Differentiate Right Side: Differentiate the left side of the equation with respect to x: The derivative of -2y^(3) with respect to x is -6y^(2)(dy)/(dx) because y is a function of x. The derivative of -x^(3) with respect to x is -3x^(2).Combine Derivatives: Differentiate the right side of the equation with respect to x: The derivative of 5xy with respect to x is 5y + 5x(dy)/(dx) by using the product rule.Solve for (dy)/(dx): Now we combine the derivatives from both sides to form the equation: -6y^(2)(dy)/(dx) - 3x^(2) = 5y + 5x(dy)/(dx).Factor Out (dy)/(dx): We need to solve for (dy)/(dx). To do this, we'll move all terms involving (dy)/(dx) to one side and the rest to the other side: -6y^(2)(dy)/(dx) - 5x(dy)/(dx) = 5y + 3x^(2).Divide to Solve (dy)/(dx): Factor out (dy)/(dx) from the left side of the equation: (dy)/(dx)(-6y^(2) - 5x) = 5y + 3x^(2).Now, divide both sides by (-6y^(2) - 5x) to solve for (dy)/(dx): (dy)/(dx) = (5y + 3x^(2)) / (-6y^(2) - 5x).

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If
-2y^(3)-x^(3)=5xy then find
(dy)/(dx) in terms of
x and
y.
Answer:
(dy)/(dx)=

If $-2 y^{3}-x^{3}=5 x y$ then find $\frac{d y}{d x}$ in terms of $x$ and $y$ . $\newline$ Answer: $\frac{d y}{d x}=$

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Q. If

-2 y^{3}-x^{3}=5 x y

then find

\frac{d y}{d x}

in terms of

x

and

y

\newline

Answer:

\frac{d y}{d x}=

Differentiate Left Side: We are given the equation $-2y^{3} - x^{3} = 5xy$ . To find $\frac{dy}{dx}$ , we need to differentiate both sides of the equation with respect to $x$ , using implicit differentiation.
Differentiate Right Side: Differentiate the left side of the equation with respect to $x$ : $\newline$ The derivative of $-2y^{3}$ with respect to $x$ is $-6y^{2}\frac{dy}{dx}$ because $y$ is a function of $x$ . $\newline$ The derivative of $-x^{3}$ with respect to $x$ is $-3x^{2}$ .
Combine Derivatives: Differentiate the right side of the equation with respect to $x$ : The derivative of $5xy$ with respect to $x$ is $5y + 5x\frac{dy}{dx}$ by using the product rule.
Solve for (\frac{dy}{dx}): Now we combine the derivatives from both sides to form the equation:\(\newline\(-6y^{ $2$ }(\frac{dy}{dx}) - $3$ x^{ $2$ } = $5$ y + $5$ x(\frac{dy}{dx}).
Factor Out $(dy)/(dx)$ : We need to solve for $(dy)/(dx)$ . To do this, we'll move all terms involving $(dy)/(dx)$ to one side and the rest to the other side: $\newline$ $-6y^{2}(dy)/(dx) - 5x(dy)/(dx) = 5y + 3x^{2}$ .
Divide to Solve $(\frac{dy}{dx}):</b> Factor out \$(\frac{dy}{dx})$ from the left side of the equation: $\newline$ $(\frac{dy}{dx})(-6y^{2} - 5x) = 5y + 3x^{2}$ .
Divide to Solve $(dy)/(dx)$ : Factor out $(dy)/(dx)$ from the left side of the equation: $\newline$ $(dy)/(dx)(-6y^{2} - 5x) = 5y + 3x^{2}$ .Now, divide both sides by $(-6y^{2} - 5x)$ to solve for $(dy)/(dx)$ : $\newline$ $(dy)/(dx) = (5y + 3x^{2}) / (-6y^{2} - 5x)$ .

If $-2 y^{3}-x^{3}=5 x y$ then find $\frac{d y}{d x}$ in terms of $x$ and $y$ . $\newline$ Answer: $\frac{d y}{d x}=$

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If $-2 y^{3}-x^{3}=5 x y$ then find $\frac{d y}{d x}$ in terms of $x$ and $y$ . $\newline$ Answer: $\frac{d y}{d x}=$