Find the Derivative Using Quotient Rule - d/dx 1/(x^2)

Problem

d()/d(x)1/(x^2)

Solution

1. Identify the numerator u=1 and the denominator v=x^2 to apply the quotient rule.

2. Differentiate the components to find d(u)/d(x)=0 and d(v)/d(x)=2*x

3. Apply the formula for the quotient rule, which is (vd(u)/d(x)−ud(v)/d(x))/(v^2)

4. Substitute the values into the formula: ((x^2)*(0)−(1)*(2*x))/((x^2)^2)

5. Simplify the numerator and the denominator to get (−2*x)/(x^4)

6. Reduce the fraction by dividing both the numerator and denominator by x

Final Answer

d()/d(x)1/(x^2)=−2/(x^3)

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