\[ \frac{d y}{d x}=\frac{330 x^{9}-88 x^{21} y}{4 x^{22}+7 y^{6}} \] Now, find the equation of the tangent line to the curve at $(1,1)$. Write your answer in $m x+b$ format

Step 1 ：The derivative of the function is given by \(\frac{d y}{d x} = \frac{330 x^{9}-88 x^{21} y}{4 x^{22}+7 y^{6}}\).

Step 2 ：We need to find the slope of the tangent line at the point (1,1). This is given by the derivative of the function at the point (1,1).

Step 3 ：Substituting x = 1 and y = 1 into the derivative, we find that the slope of the tangent line is 22.

Step 4 ：The equation of a tangent line to a curve at a given point is given by \(y - y_1 = m(x - x_1)\), where \((x_1, y_1)\) is the point of tangency and m is the slope of the tangent line.

Step 5 ：Substituting \((x_1, y_1) = (1,1)\) and \(m = 22\) into the equation, we find that the equation of the tangent line is \(y = 22x - 21\).

Step 6 ：\(\boxed{y = 22x - 21}\) is the equation of the tangent line to the curve at the point (1,1).