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

Let's go through each equation step by step to find .### (a) To find , we'll differentiate both sides of the equation with respect to : Using the product rule and chain rule, we get: Now, collect the terms involving : Finally, solve for : ### (b) Differentiate both sides with respect to : Using the product rule and chain rule, we get: Collect the terms involving : Finally, solve for : ### (c) Differentiate both sides with respect to : Using the product rule and chain rule, we get: Collect the terms involving : Finally, solve for : ### (d) \(e^{xy^2} = 10(x^2 + y^2)\)Differentiate both sides with respect to : Using the chain rule, we get: Collect the terms involving : Finally, solve for : These are the derivatives for each of the given equations.