Using implicit differentiation, find (dy)/(dx). -7x^(2)y^(4)-5xy^(2)=4-4x

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Using implicit differentiation, find  (dy)/(dx).  -7x^(2)y^(4)-5xy^(2)=4-4x

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Apply Implicit Differentiation: To find the derivative (dy)/(dx) using implicit differentiation, we need to differentiate both sides of the equation with respect to x, treating y as a function of x. This means we will apply the product rule to terms involving both x and y, and the chain rule to terms involving y.Differentiate -7x^(2)y^(4): Differentiate the term -7x^(2)y^(4) with respect to x. Using the product rule, we get the derivative of the first function times the second function plus the first function times the derivative of the second function. The derivative of x^(2) is 2x, and the derivative of y^(4) with respect to x is 4y^(3)(dy/dx) by the chain rule. So, the derivative of -7x^(2)y^(4) is -7[2xy^(4) + x^(2)*4y^(3)(dy/dx)].Differentiate -5xy^(2): Differentiate the term -5xy^(2) with respect to x. Again, using the product rule, we get the derivative of the first function times the second function plus the first function times the derivative of the second function. The derivative of x is 1, and the derivative of y^(2) with respect to x is 2y(dy/dx) by the chain rule. So, the derivative of -5xy^(2) is -5[y^(2) + x*2y(dy/dx)].Differentiate 4-4x: Differentiate the right side of the equation, 4-4x, with respect to x. The derivative of a constant is 0, and the derivative of -4x with respect to x is -4. So, the derivative of 4-4x is 0 - 4.Combine and Simplify: Combine the derivatives from the previous steps to write the differentiated equation: -7[2xy^(4) + x^(2)*4y^(3)(dy/dx)] - 5[y^(2) + x*2y(dy/dx)] = -4.Isolate Terms: Simplify the equation by distributing the constants and combining like terms: -14xy^(4) - 28x^(2)y^(3)(dy/dx) - 5y^(2) - 10xy(dy/dx) = -4.Factor Out (dy/dx): Isolate terms with (dy/dx) on one side and the rest on the other side: -28x^(2)y^(3)(dy/dx) - 10xy(dy/dx) = 4 + 14xy^(4) + 5y^(2).Solve for (dy/dx): Factor out (dy/dx) from the left side of the equation: (dy/dx)(-28x^(2)y^(3) - 10xy) = 4 + 14xy^(4) + 5y^(2).Solve for (dy/dx) by dividing both sides of the equation by (-28x^(2)y^(3) - 10xy): (dy/dx) = (4 + 14xy^(4) + 5y^(2)) / (-28x^(2)y^(3) - 10xy).

Using implicit differentiation, find $\frac{dy}{dx}$ . $\newline$ $-7x^{2}y^{4}-5xy^{2}=4-4x$

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Using implicit differentiation, find dydx\frac{dy}{dx}dxdy​.\newline−7x2y4−5xy2=4−4x-7x^{2}y^{4}-5xy^{2}=4-4x−7x2y4−5xy2=4−4x

Using implicit differentiation, find $\frac{dy}{dx}$ . $\newline$ $-7x^{2}y^{4}-5xy^{2}=4-4x$