Find the Derivative - d/dx 2x^2+x-1

Problem

d()/d(x)*(2*x2+x−1)

Solution

1. Apply the sum rule for derivatives, which allows for the differentiation of each term individually.

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

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

(d(2)*x2)/d(x)=2⋅2*x(2−1)=4*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. Apply the constant rule to the third term, as the derivative of any constant is zero.

d(1)/d(x)=0

5. Combine the results to find the final derivative expression.

4*x+1−0=4*x+1

Final Answer

d()/d(x)*(2*x2+x−1)=4*x+1

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