Find the Derivative - d/dx x^2y

Problem

d()/d(x)*x2*y

Solution

1. Identify the rule needed for differentiation. Since x2 and y are multiplied and y is assumed to be a function of x use the product rule.

2. Apply the product rule, which states that d()/d(x)*[ƒ(x)*g(x)]=ƒ(x)′*g(x)+ƒ(x)*g(x)′

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

4. Differentiate the second term y with respect to x to get d(y)/d(x)

5. Combine the results into the final expression.

Final Answer

d()/d(x)*x2*y=2*x*y+x2d(y)/d(x)

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