Find the Derivative - d/dx 2x^2-5x+3

Problem

d()/d(x)*(2*x2−5*x+3)

Solution

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

d()/d(x)*(2*x2−5*x+3)=(d(2)*x2)/d(x)−(d(5)*x)/d(x)+d(3)/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.

(d(5)*x)/d(x)=5⋅1*x(1−1)=5

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

d(3)/d(x)=0

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

4*x−5+0=4*x−5

Final Answer

d()/d(x)*(2*x2−5*x+3)=4*x−5

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