Find the Derivative - d/dx 8/(x^3)

Problem

d()/d(x)8/(x3)

Solution

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

8/(x3)=8*x(−3)

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

(d(8)*x(−3))/d(x)=8⋅(−3)*x(−3−1)

3. Simplify the coefficient and the exponent.

8⋅(−3)*x(−4)=−24*x(−4)

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

−24*x(−4)=−24/(x4)

Final Answer

d()/d(x)8/(x3)=−24/(x4)

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