Find the Derivative - d/dx 1/(x^8)

Problem

d()/d(x)1/(x8)

Solution

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

1/(x8)=x(−8)

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

d(x(−8))/d(x)=−8*x(−8−1)

3. Simplify the exponent by performing the subtraction.

−8*x(−8−1)=−8*x(−9)

4. Rewrite the result back into fractional form by moving the variable to the denominator.

−8*x(−9)=−8/(x9)

Final Answer

d()/d(x)1/(x8)=−8/(x9)

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