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

Problem

d()/d(x)*(x2+x)

Solution

1. Identify the function to be differentiated, which is ƒ(x)=x2+x

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

3. Apply the power rule to the first term x2 The power rule states d(xn)/d(x)=n*x(n−1)

4. Differentiate the first term: d(x2)/d(x)=2*x

5. Differentiate the second term: d(x)/d(x)=1

6. Combine the results to find the final derivative.

Final Answer

d()/d(x)*(x2+x)=2*x+1

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