Find the Derivative - d/dx f(x)=x^2-2x-3

Problem

d()/d(x)*(x2−2*x−3)

Solution

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

d()/d(x)*(x2−2*x−3)=d(x2)/d(x)−(d(2)*x)/d(x)−d(3)/d(x)

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

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

3. Apply the constant multiple rule and the power rule to the second term.

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

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 of the function.

2*x−2−0=2*x−2

Final Answer

d()/d(x)*(x2−2*x−3)=2*x−2

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