If -4y^(2)+y^(3)+2+5x^(3)=0 then find (dy)/(dx) in terms of x and y. Answer: (dy)/(dx)=

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If  -4y^(2)+y^(3)+2+5x^(3)=0 then find  (dy)/(dx) in terms of  x and  y. Answer:  (dy)/(dx)=

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Given Equation: We are given the equation -4y^(2) + y^(3) + 2 + 5x^(3) = 0 and we need to find the derivative of y with respect to x, denoted as (dy)/(dx). To do this, we will implicitly differentiate both sides of the equation with respect to x.Implicit Differentiation: Differentiate each term of the equation with respect to x. For the terms involving y, we will use the chain rule, treating y as a function of x (y = y(x)). This means that when we differentiate y terms, we multiply by (dy)/(dx) after taking the derivative with respect to y.Differentiate Terms: Differentiating -4y^(2) with respect to x gives us -8y(dy)/(dx), because the derivative of y^(2) with respect to y is 2y, and then we multiply by (dy)/(dx) due to the chain rule.Derivative of Constant: Differentiating y^(3) with respect to x gives us 3y^(2)(dy)/(dx), because the derivative of y^(3) with respect to y is 3y^(2), and then we multiply by (dy)/(dx) due to the chain rule.Combine Differentiated Terms: The derivative of the constant term 2 with respect to x is 0, because the derivative of any constant is 0.Factor Out (dy)/(dx): Differentiating 5x^(3) with respect to x gives us 15x^(2), because the derivative of x^(3) with respect to x is 3x^(2).Isolate (dy)/(dx): Putting it all together, the differentiated equation is: -8y(dy)/(dx) + 3y^(2)(dy)/(dx) + 0 + 15x^(2) = 0Final Solution: Now we need to solve for (dy)/(dx). We can factor (dy)/(dx) out of the terms that contain it: (dy)/(dx)(-8y + 3y^(2)) + 15x^(2) = 0To isolate (dy)/(dx), we move the term not containing (dy)/(dx) to the other side of the equation: (dy)/(dx)(-8y + 3y^(2)) = -15x^(2)Finally, we divide both sides of the equation by (-8y + 3y^(2)) to solve for (dy)/(dx): (dy)/(dx) = -15x^(2) / (-8y + 3y^(2))

If $-4 y^{2}+y^{3}+2+5 x^{3}=0$ 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 −4y2+y3+2+5x3=0 -4 y^{2}+y^{3}+2+5 x^{3}=0 −4y2+y3+2+5x3=0 then find dydx \frac{d y}{d x} dxdy​ in terms of x x x and y y y.\newlineAnswer: dydx= \frac{d y}{d x}= dxdy​=

If $-4 y^{2}+y^{3}+2+5 x^{3}=0$ then find $\frac{d y}{d x}$ in terms of $x$ and $y$ . $\newline$ Answer: $\frac{d y}{d x}=$