Find the Derivative - d/dx natural log of 1/x

Problem

d(ln(1/x))/d(x)

Solution

1. Apply logarithmic properties to simplify the expression before differentiating. Use the rule ln(1/a)=−ln(a)

ln(1/x)=−ln(x)

2. Rewrite the derivative using the simplified form.

d(ln(1/x))/d(x)=(d(−)*ln(x))/d(x)

3. Apply the constant multiple rule by moving the negative sign outside the derivative.

(d(−)*ln(x))/d(x)=−d(ln(x))/d(x)

4. Differentiate the natural logarithm using the standard rule d(ln(x))/d(x)=1/x

−d(ln(x))/d(x)=−1/x

Final Answer

d(ln(1/x))/d(x)=−1/x

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