Find the Derivative - d/dx (2x-1)^3

Problem

d(2*x−1)/d(x)

Solution

1. Identify the rule needed for the derivative. Since the expression is a function raised to a power, use the Chain Rule, which states d(un)/d(x)=n*u(n−1)⋅d(u)/d(x)

2. Apply the Power Rule to the outer function. Bring the exponent 3 to the front and decrease the exponent by 1

3*(2*x−1)2⋅d(2*x−1)/d(x)

3. Differentiate the inner function 2*x−1 with respect to x

d(2*x−1)/d(x)=2

4. Multiply the results together to find the final derivative.

3*(2*x−1)2⋅2

5. Simplify the expression by multiplying the constants.

6*(2*x−1)2

Final Answer

d(2*x−1)/d(x)=6*(2*x−1)2

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