Find the Derivative - d/dx xy^3

Problem

(d(x)*y^3)/d(x)

Solution

1. Identify the rule needed for the expression x*y^3 which is a product of two functions x and y^3

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 x with respect to x which equals 1

4. Differentiate the second term y^3 with respect to x using the chain rule (implicit differentiation), which results in 3*y^2d(y)/d(x)

5. Combine the parts into the final derivative expression.

Final Answer

(d(x)*y^3)/d(x)=3*x*y^2d(y)/d(x)+y^3

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