Find (dy)/(dx) given: (a) xy^3-2x^2y^2+x^4=1 (b) x^2siny-ycosx=10x^3 xcosy-y^2sinx=2 (d) e^xy^(2)=10(x^2+y^2) ln(x^2+sqrt (y))=sin(xy^2)

To find for each equation, we will differentiate both sides of each equation with respect to using implicit differentiation.(a) Differentiating both sides with respect to , we get: Simplifying, we have: Therefore, the derivative is: (b) Differentiating both sides with respect to , we get: Simplifying, we have: Therefore, the derivative is: (c) Differentiating both sides with respect to , we get: Simplifying, we have: Therefore, the derivative is: (d) Differentiating both sides with respect to , we get: Simplifying, we have: Therefore, the derivative is: (e) Differentiating both sides with respect to , we get: Simplifying, we have: Therefore, the derivative is: