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

Problem

d()/d(x)*(x−x2)

Solution

1. Identify the expression as a difference of two terms, x and x2

2. Apply the sum/difference rule for derivatives, which states that the derivative of a sum or difference is the sum or difference of the derivatives.

d()/d(x)*(x−x2)=d(x)/d(x)−d(x2)/d(x)

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

4. Differentiate the first term, x which results in 1

5. Differentiate the second term, x2 which results in 2*x

6. Combine the results to find the final derivative.

Final Answer

d()/d(x)*(x−x2)=1−2*x

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