Find the Derivative - d/dx f(x)=x^5

Problem

d(x5)/d(x)

Solution

1. Identify the function as a power function of the form xn where n=5

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

3. Substitute the value n=5 into the power rule formula.

4. Simplify the exponent by calculating 5 - 1 = 4$.

Final Answer

d(x5)/d(x)=5*x4

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