Find the Derivative - d/dx 9/(x^2)

Problem

d()/d(x)9/(x2)

Solution

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

9/(x2)=9*x(−2)

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

(d(9)*x(−2))/d(x)=9⋅(−2)*x(−2−1)

3. Simplify the coefficients and the exponent.

9⋅(−2)*x(−3)=−18*x(−3)

4. Rewrite the result with a positive exponent by moving the variable back to the denominator.

−18*x(−3)=−18/(x3)

Final Answer

d()/d(x)9/(x2)=−18/(x3)

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