Find the Derivative - d/dx y=8/(3x^2)

Problem

d()/d(x)8/(3*x2)

Solution

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

8/(3*x2)=8/3*x(−2)

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

d()/d(x)8/3*x(−2)=8/3⋅(−2)*x(−2−1)

3. Simplify the coefficients and the exponent.

8/3⋅(−2)*x(−3)=−16/3*x(−3)

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

−16/3*x(−3)=−16/(3*x3)

Final Answer

d()/d(x)8/(3*x2)=−16/(3*x3)

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