Find the Derivative - d/dx xy^2

Problem

d()/d(x)*x*y2

Solution

1. Identify the rule needed for the expression x*y2 which is a product of two functions x and y2

2. Apply the product rule, which states d()/d(x)*u*v=ud(v)/d(x)+vd(u)/d(x)

3. Differentiate the first term x with respect to x which is 1

4. Differentiate the second term y2 with respect to x using the chain rule (implicit differentiation), which results in 2*yd(y)/d(x)

5. Combine the results into the product rule formula.

Final Answer

d()/d(x)*x*y2=2*x*yd(y)/d(x)+y2

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