Find the Derivative - d/dx 6x-x^2

Problem

d()/d(x)*(6*x−x2)

Solution

1. Identify the expression as a difference of two terms, 6*x and x2

2. Apply the sum/difference rule for derivatives, which allows for differentiating each term individually.

3. Apply the power rule to the first term, where (d(a)*x)/d(x)=a

(d(6)*x)/d(x)=6

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

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

5. Combine the results to find the final derivative.

Final Answer

d()/d(x)*(6*x−x2)=6−2*x

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