Find the Derivative - d/d@VAR f(x)=1/(x^3)

Problem

d()/d(x)1/(x3)

Solution

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

1/(x3)=x(−3)

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

d(x(−3))/d(x)=−3*x(−3−1)

3. Simplify the exponent by performing the subtraction.

−3*x(−3−1)=−3*x(−4)

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

−3*x(−4)=−3/(x4)

Final Answer

d()/d(x)1/(x3)=−3/(x4)

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