Find the Derivative - d/dx f(x)=(x+8)^(2/3)

Problem

d()/d(x)*(x+8)(2/3)

Solution

1. Identify the rule needed for the differentiation, which is the Power Rule combined with the Chain Rule.

2. Apply the Power Rule by bringing the exponent 2/3 to the front and subtracting 1 from the exponent.

d(x+8)/d(x)=2/3*(x+8)(2/3−1)⋅d(x+8)/d(x)

3. Differentiate the inner function x+8 with respect to x which results in 1

d(x+8)/d(x)=1

4. Simplify the exponent and the expression.

2/3−1=−1/3

5. Combine the results to find the final derivative.

2/3*(x+8)(−1/3)⋅1=2/(3*(x+8)(1/3))

Final Answer

d(x+8)/d(x)=2/(3*(x+8)(1/3))

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