Find the Derivative - d/d@VAR f(x)=3x^2-x

Problem

d()/d(x)*(3*x2−x)

Solution

1. Identify the function to be differentiated, which is ƒ(x)=3*x2−x

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

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

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

(d(3)*x2)/d(x)=3⋅2*x(2−1)=6*x

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

d(x)/d(x)=1*x(1−1)=1

5. Combine the results to find the final derivative.

6*x−1

Final Answer

d(3*x2−x)/d(x)=6*x−1

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