Find the Derivative - d/d@VAR f(x)=1/(x^6)

Problem

d()/d(x)1/(x6)

Solution

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

1/(x6)=x(−6)

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

d(x(−6))/d(x)=−6*x(−6−1)

3. Simplify the exponent by performing the subtraction.

−6*x(−6−1)=−6*x(−7)

4. Convert the expression back into a fraction by moving the variable with the negative exponent to the denominator.

−6*x(−7)=−6/(x7)

Final Answer

d()/d(x)1/(x6)=−6/(x7)

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