Find the Derivative - d/dx f(x)=1/(x^2)

Problem

d()/d(x)1/(x2)

Solution

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

1/(x2)=x(−2)

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

d(x(−2))/d(x)=−2*x(−2−1)

3. Simplify the exponent by performing the subtraction.

−2*x(−2−1)=−2*x(−3)

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

−2*x(−3)=−2/(x3)

Final Answer

d()/d(x)1/(x2)=−2/(x3)

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