Find the Derivative - d/dx x^2y^2

Problem

(d(x2)*y2)/d(x)

Solution

1. Identify the rule needed for the expression x2*y2 which is the product rule since it is a product of two functions.

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

3. Differentiate the first term x2 with respect to x to get 2*x

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

5. Combine the results into the product rule formula.

6. Simplify the expression by factoring out common terms if necessary.

Final Answer

(d(x2)*y2)/d(x)=2*x*y2+2*x2*yd(y)/d(x)

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