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

Problem

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

Solution

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

3/(2*x)=3/2*x(−1)

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

d()/d(x)3/2*x(−1)=3/2d(x(−1))/d(x)

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

3/2*(−1*x(−2))

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

−3/2*x(−2)=−3/(2*x2)

Final Answer

d()/d(x)3/(2*x)=−3/(2*x2)

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