Find the Derivative - d/dx 1/(3x^3)

Problem

d()/d(x)1/(3*x3)

Solution

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

1/(3*x3)=1/3*x(−3)

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

d()/d(x)1/3*x(−3)=1/3⋅(−3)*x(−3−1)

3. Simplify the coefficient by multiplying the fraction and the integer.

1/3⋅(−3)=−1

4. Simplify the exponent and rewrite the expression with a positive exponent.

−1*x(−4)=−1/(x4)

Final Answer

d()/d(x)1/(3*x3)=−1/(x4)

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