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

Problem

d()/d(x)*x^8

Solution

1. Identify the function as a power function of the form x^n where n=8

2. Apply the power rule for differentiation, which states that d(x^n)/d(x)=n*x^(n−1)

3. Substitute the value of n into the formula to get 8*x^(8−1)

4. Simplify the exponent by subtracting 1 from 8 to get 7.

Final Answer

d(x^8)/d(x)=8*x^7

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