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

Problem

d()/d(x)*(x2+x−5)

Solution

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

2. Apply the sum rule for derivatives, which allows for the differentiation of each term individually: d(x2)/d(x)+d(x)/d(x)−d(5)/d(x)

3. Apply the power rule to the first two terms, where d(xn)/d(x)=n*x(n−1) For x2 the derivative is 2*x For x the derivative is 1

4. Apply the constant rule to the final term, noting that the derivative of any constant is 0

5. Combine the results to find the final derivative.

Final Answer

d(x2+x−5)/d(x)=2*x+1

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