Find the Derivative - d/dx 2x^2-7x+5

Problem

d()/d(x)*(2*x2−7*x+5)

Solution

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

(d(2)*x2)/d(x)−(d(7)*x)/d(x)+d(5)/d(x)

2. Apply the power rule to the first term, where d(xn)/d(x)=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.

(d(7)*x)/d(x)=7⋅1*x(1−1)=7

4. Apply the constant rule to the third term, noting that the derivative of any constant is zero.

d(5)/d(x)=0

5. Combine the results to find the final derivative.

4*x−7+0=4*x−7

Final Answer

d()/d(x)*(2*x2−7*x+5)=4*x−7

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