Find the Derivative - d/dx 1/(4x)

Problem

d()/d(x)1/(4*x)

Solution

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

1/(4*x)=1/4*x(−1)

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

d()/d(x)1/4*x(−1)=1/4d(x(−1))/d(x)

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

1/4*(−1*x(−1−1))=−1/4*x(−2)

4. Simplify the expression by moving the variable back to the denominator with a positive exponent.

−1/4*x(−2)=−1/(4*x2)

Final Answer

d()/d(x)1/(4*x)=−1/(4*x2)

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