Find the Derivative - d/dx 3x^2-x

Problem

d()/d(x)*(3*x2−x)

Solution

1. Apply the sum/difference rule of differentiation, which allows for the derivative of each term to be taken separately.

d()/d(x)*(3*x2−x)=(d(3)*x2)/d(x)−d(x)/d(x)

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

(d(3)*x2)/d(x)=2⋅3*x(2−1)=6*x

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

d(x)/d(x)=1⋅x(1−1)=1

4. Combine the results to find the final derivative.

6*x−1

Final Answer

d()/d(x)*(3*x2−x)=6*x−1

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