Find the Derivative - d/dx -5/(x^2)

Problem

d()/d(x)(−5)/(x2)

Solution

1. Rewrite the expression using a negative exponent to make it easier to apply the power rule.

(−5)/(x2)=−5*x(−2)

2. Apply the power rule for derivatives, 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)=10

−2−1=−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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