Find the Derivative - d/d@VAR f(x)=2x^2-7x+5

Problem

d()/d(x)*(2*x2−7*x+5)

Solution

1. Identify the function to be differentiated, which is a polynomial ƒ(x)=2*x2−7*x+5

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

3. Apply the power rule to the first term 2*x2 where d(xn)/d(x)=n*x(n−1)

(d(2)*x2)/d(x)=4*x

4. Apply the power rule to the second term −7*x

(d(−)*7*x)/d(x)=−7

5. Apply the constant rule to the third term 5 noting that the derivative of any constant is 0

d(5)/d(x)=0

6. Combine the results of the individual derivatives to find the final expression.

Final Answer

d()/d(x)*(2*x2−7*x+5)=4*x−7

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