Find the Derivative - d/d@VAR f(x)=x^3+x^2

Problem

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

Solution

1. Identify the function to be differentiated, which is a sum of two power terms: ƒ(x)=x^3+x^2

2. Apply the sum rule for derivatives, which states that the derivative of a sum is the sum of the derivatives: d()/d(x)*(x^3+x^2)=d(x^3)/d(x)+d(x^2)/d(x)

3. Apply the power rule to each term, where d(x^n)/d(x)=n*x^(n−1)

4. Differentiate the first term: d(x^3)/d(x)=3*x^(3−1)=3*x^2

5. Differentiate the second term: d(x^2)/d(x)=2*x^(2−1)=2*x^1=2*x

6. Combine the results to find the final derivative.

Final Answer

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

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