If -y^(2)=x^(2)-x+3y^(3) then find (dy)/(dx) at the point (-4,-2). Answer: (dy)/(dx)|_((-4,-2))=

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If  -y^(2)=x^(2)-x+3y^(3) then find  (dy)/(dx) at the point  (-4,-2). Answer:  (dy)/(dx)|_((-4,-2))=

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Differentiate Left Side: First, we need to differentiate both sides of the equation with respect to x to find dy/dx. The equation is -y^2 = x^2 - x + 3y^3. We will use implicit differentiation because y is a function of x.Differentiate Right Side: Differentiate the left side of the equation with respect to x: d(-y^2)/dx = -2y * (dy/dx).Equate Derivatives: Differentiate the right side of the equation with respect to x: d(x^2 - x + 3y^3)/dx = 2x - 1 + 3 * 3y^2 * (dy/dx) because we need to use the chain rule for the term 3y^3.Rearrange Equation: Now we equate the derivatives from the left and right sides: -2y * (dy/dx) = 2x - 1 + 9y^2 * (dy/dx).Isolate dy/dx: Rearrange the equation to solve for dy/dx: (dy/dx) * (9y^2 + 2y) = 2x - 1.Substitute Point: Isolate dy/dx: (dy/dx) = (2x - 1) / (9y^2 + 2y).Calculate Numerator: Now we substitute the point (-4, -2) into the equation to find the value of dy/dx at that point: (dy/dx)|_((-4,-2)) = (2*(-4) - 1) / (9*(-2)^2 + 2*(-2)).Calculate Denominator: Calculate the numerator: 2*(-4) - 1 = -8 - 1 = -9.Divide Numerator: Calculate the denominator: 9*(-2)^2 + 2*(-2) = 9*4 - 4 = 36 - 4 = 32.Now divide the numerator by the denominator to get the value of dy/dx at the point (-4, -2): (dy/dx)|_((-4,-2)) = -9 / 32.

If $-y^{2}=x^{2}-x+3 y^{3}$ then find $\frac{d y}{d x}$ at the point $(-4,-2)$ . $\newline$ Answer: $\left.\frac{d y}{d x}\right|_{(-4,-2)}=$

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If −y2=x2−x+3y3 -y^{2}=x^{2}-x+3 y^{3} −y2=x2−x+3y3 then find dydx \frac{d y}{d x} dxdy​ at the point (−4,−2) (-4,-2) (−4,−2).\newlineAnswer: dydx∣(−4,−2)= \left.\frac{d y}{d x}\right|_{(-4,-2)}= dxdy​∣∣​(−4,−2)​=

If $-y^{2}=x^{2}-x+3 y^{3}$ then find $\frac{d y}{d x}$ at the point $(-4,-2)$ . $\newline$ Answer: $\left.\frac{d y}{d x}\right|_{(-4,-2)}=$