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

Problem

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

Solution

1. Identify the rule needed for the expression, which is the sum rule for derivatives.

2. Apply the sum rule by taking the derivative of each term individually.

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

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

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

4. Apply the power rule to the second term, noting that x is x1

d(x)/d(x)=1

5. Combine the results to find the final derivative.

2*x+1

Final Answer

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

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