Find the Derivative - d/d@VAR f(x)=5/(x^2)

Problem

d()/d(x)5/(x2)

Solution

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

5/(x2)=5*x(−2)

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

(d(5)*x(−2))/d(x)=5⋅(−2)*x(−2−1)

3. Simplify the coefficients and the exponent.

5⋅(−2)*x(−3)=−10*x(−3)

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

−10*x(−3)=−10/(x3)

Final Answer

d()/d(x)5/(x2)=−10/(x3)

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