Find the Derivative - d/dx (2x-1)^5

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. Differentiate the outer function by applying the Power Rule to the exponent 5

d(2*x−1)/d(x)=5*(2*x−1)(5−1)⋅d(2*x−1)/d(x)

3. Simplify the exponent and find the derivative of the inner function 2*x−1

d(2*x−1)/d(x)=2

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

5*(2*x−1)4⋅2=10*(2*x−1)4

Final Answer

d(2*x−1)/d(x)=10*(2*x−1)4

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