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

Problem

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

Solution

1. Identify the rule needed for the derivative, which is the Chain Rule for a function of the form un

2. Apply the Power Rule to the outer function by bringing the exponent 2 to the front and decreasing the power by 1

2*(2*x+1)(2−1)

3. Apply the Chain Rule by multiplying by the derivative of the inner function 2*x+1

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

4. Differentiate the inner expression 2*x+1 which results in 2

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

5. Simplify the expression by multiplying the constants.

2*(2*x+1)⋅2=4*(2*x+1)

6. Distribute the constant to reach the final simplified form.

4*(2*x+1)=8*x+4

Final Answer

d(2*x+1)/d(x)=8*x+4

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