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

Problem

d(2*x−1)/d(x)

Solution

1. Identify the rule needed to differentiate the expression, which is the power rule combined with the chain rule.

2. Apply the power rule by bringing the exponent 2 to the front and decreasing the exponent by 1

2*(2*x−1)(2−1)

3. Apply the chain rule by multiplying the result 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 function 2*x−1 which results in 2

d(2*x−1)/d(x)=2

5. Multiply the components together to find the final derivative.

2*(2*x−1)⋅2

6. Simplify the expression by distributing the constants.

4*(2*x−1)=8*x−4

Final Answer

d(2*x−1)/d(x)=8*x−4

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