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

Problem

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

Solution

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

2. Apply the sum rule for derivatives, which states that the derivative of a sum is the sum of the derivatives: d()/d(x)*(2*x2+5*x)=(d(2)*x2)/d(x)+(d(5)*x)/d(x)

3. Apply the power rule and the constant multiple rule to the first term: (d(2)*x2)/d(x)=2⋅2*x(2−1)=4*x

4. Apply the power rule to the second term: (d(5)*x)/d(x)=5⋅1*x(1−1)=5

5. Combine the results to find the final derivative.

Final Answer

d()/d(x)*(2*x2+5*x)=4*x+5

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