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

Problem

d()/d(x)1/(5*x5)

Solution

1. Rewrite the expression using a negative exponent to make it easier to differentiate.

1/(5*x5)=1/5*x(−5)

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

d()/d(x)1/5*x(−5)=1/5⋅(−5)*x(−5−1)

3. Simplify the coefficient by multiplying 1/5 and −5

1/5⋅(−5)=−1

4. Simplify the exponent and rewrite the expression with a positive exponent.

−1*x(−6)=−1/(x6)

Final Answer

d()/d(x)1/(5*x5)=−1/(x6)

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