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 coefficient and the exponent.

2⋅(−3)*x(−4)=−6*x(−4)

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

−6*x(−4)=−6/(x4)

Final Answer

d()/d(x)2/(x3)=−6/(x4)

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