Find the Derivative - d/dx -2/(x^3)

Problem

d()/d(x)(−2)/(x3)

Solution

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

(−2)/(x3)=−2*x(−3)

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

(d(−)*2*x(−3))/d(x)=−2⋅(−3)*x(−3−1)

3. Simplify the coefficients and the exponent.

−2⋅(−3)=6

−3−1=−4

6*x(−4)

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

6*x(−4)=6/(x4)

Final Answer

d()/d(x)(−2)/(x3)=6/(x4)

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