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

Problem

d(x+1)/d(x)

Solution

1. Identify the rule needed to differentiate the expression. Since the function is a composition of an outer power function u4 and an inner linear function u=x+1 use the Chain Rule.

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)(4−1)⋅d(x+1)/d(x)

3. Differentiate the inner function with respect to x The derivative of x+1 is 1

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

4. Multiply the results together 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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