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

Problem

d()/d(x)*(x^2+x−3)

Solution

1. Identify the expression as a sum of three terms and apply the sum rule for derivatives, which allows for differentiating each term individually.

d()/d(x)*(x^2+x−3)=d(x^2)/d(x)+d(x)/d(x)−d(3)/d(x)

2. Apply the power rule to the first term x^2 The power rule states that d(x^n)/d(x)=n*x^(n−1)

d(x^2)/d(x)=2*x

3. Apply the power rule to the second term x Since x is x^1 the derivative is 1*x^0

d(x)/d(x)=1

4. Apply the constant rule to the third term 3 The derivative of any constant is zero.

d(3)/d(x)=0

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

2*x+1−0=2*x+1

Final Answer

d()/d(x)*(x^2+x−3)=2*x+1

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