Find the Derivative - d/dx (x-1)^4

Problem

d(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 4 to the front and decrease the exponent by 1

d(x−1)/d(x)=4*(x−1)3⋅d(x−1)/d(x)

3. Differentiate the inner function (x−1) with respect to x

d(x−1)/d(x)=1

4. Multiply the results to find the final derivative.

4*(x−1)3⋅1=4*(x−1)3

Final Answer

d(x−1)/d(x)=4*(x−1)3

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