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

Problem

d()/d(x)3/(x3)

Solution

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

3/(x3)=3*x(−3)

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

(d(3)*x(−3))/d(x)=3⋅(−3)*x(−3−1)

3. Simplify the coefficients and the exponent.

3⋅(−3)*x(−4)=−9*x(−4)

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

−9*x(−4)=−9/(x4)

Final Answer

d()/d(x)3/(x3)=−9/(x4)

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