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

Problem

d()/d(x)2/(3*x2)

Solution

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

2/(3*x2)=2/3*x(−2)

2. Apply the constant multiple rule, which allows the constant factor to be moved outside the derivative.

d()/d(x)2/3*x(−2)=2/3d(x(−2))/d(x)

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

2/3*(−2*x(−3))

4. Simplify the resulting expression by multiplying the constants and rewriting the negative exponent as a fraction.

−4/3*x(−3)=−4/(3*x3)

Final Answer

d()/d(x)2/(3*x2)=−4/(3*x3)

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