Find the Derivative - d/dx y=1/(x^5)

Problem

d()/d(x)1/(x5)

Solution

1. Rewrite the expression using a negative exponent to prepare for the power rule.

1/(x5)=x(−5)

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

d(x(−5))/d(x)=−5*x(−5−1)

3. Simplify the exponent by performing the subtraction.

−5*x(−5−1)=−5*x(−6)

4. Rewrite the result with a positive exponent by moving the variable to the denominator.

−5*x(−6)=−5/(x6)

Final Answer

d()/d(x)1/(x5)=−5/(x6)

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