Find the Derivative - d/dx x^2+2x+1

Problem

d()/d(x)*(x^2+2*x+1)

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(x^2)+2*x+1)/d(x)=d(x^2)/d(x)+(d(2)*x)/d(x)+d(1)/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 constant multiple rule and the power rule to the second term 2*x

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

4. Apply the constant rule to the third term 1 The derivative of any constant is zero.

d(1)/d(x)=0

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

2*x+2+0=2*x+2

Final Answer

(d(x^2)+2*x+1)/d(x)=2*x+2

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