Find the Derivative - d/dx 1/(x^7)

Problem

d()/d(x)1/(x7)

Solution

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

1/(x7)=x(−7)

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

d(x(−7))/d(x)=−7*x(−7−1)

3. Simplify the exponent by performing the subtraction.

−7*x(−7−1)=−7*x(−8)

4. Rewrite the result back into fraction form by moving the variable with the negative exponent to the denominator.

−7*x(−8)=−7/(x8)

Final Answer

d()/d(x)1/(x7)=−7/(x8)

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