Find the Derivative - d/dx 2/(3x)

Problem

d()/d(x)2/(3*x)

Solution

1. Rewrite the expression using a negative exponent to make it easier to apply the power rule.

2/(3*x)=2/3*x(−1)

2. Apply the constant multiple rule by moving the constant coefficient outside the derivative.

d()/d(x)2/3*x(−1)=2/3d(x(−1))/d(x)

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

2/3*(−1*x(−2))

4. Simplify the expression by multiplying the constants and moving the variable back to the denominator.

−2/(3*x2)

Final Answer

d()/d(x)2/(3*x)=−2/(3*x2)

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