Using implicit differentiation, find (dy)/(dx). sin(xy)=2x^(4)y^(3)+4

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Using implicit differentiation, find  (dy)/(dx).  sin(xy)=2x^(4)y^(3)+4

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Apply Chain and Product Rule: Differentiate both sides of the equation with respect to x using implicit differentiation. The left side of the equation is sin(xy), which is a product of x and y, so we will need to use the product rule in combination with the chain rule. The right side of the equation is 2x^4y^3 + 4, which is a sum of terms involving products of x and y, so we will also need to use the product rule there.Differentiate sin(xy): Differentiate the left side, sin(xy), with respect to x. Using the chain rule, the derivative of sin(u) with respect to u is cos(u), and then we multiply by the derivative of u with respect to x, where u = xy. This gives us cos(xy) * (y + x(dy/dx)).Differentiate 2x^4y^3 + 4: Differentiate the right side, 2x^4y^3 + 4, with respect to x. Using the product rule, the derivative of 2x^4y^3 with respect to x is 2 * (4x^3y^3 + x^4 * 3y^2(dy/dx)). The derivative of the constant 4 with respect to x is 0.Write Differentiated Equation: Write down the differentiated equation. cos(xy) * (y + x(dy/dx)) = 2 * (4x^3y^3 + x^4 * 3y^2(dy/dx)) + 0Solve for (dy/dx): Solve for (dy/dx). We need to collect all terms involving (dy/dx) on one side and the rest on the other side to solve for (dy/dx). cos(xy) * x(dy/dx) - 2x^4 * 3y^2(dy/dx) = 2 * 4x^3y^3 - cos(xy) * yFactor out (dy/dx): Factor out (dy/dx) from the terms on the left side. (dy/dx)(x * cos(xy) - 2x^4 * 3y^2) = 2 * 4x^3y^3 - cos(xy) * yIsolate (dy/dx): Isolate (dy/dx). (dy/dx) = (2 * 4x^3y^3 - cos(xy) * y) / (x * cos(xy) - 2x^4 * 3y^2)Simplify (dy/dx): Simplify the expression for (dy/dx). (dy/dx) = (8x^3y^3 - cos(xy) * y) / (x * cos(xy) - 6x^4y^2)

Using implicit differentiation, find $\frac{dy}{dx}$ . $\sin(xy) = 2x^{4}y^{3} + 4$

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Using implicit differentiation, find $\frac{dy}{dx}$ . $\sin(xy) = 2x^{4}y^{3} + 4$