# Find the Derivative – d/dx log of 1/x

Differentiate using the chain rule, which states that is where and .
To apply the Chain Rule, set as .
The derivative of with respect to is .
Replace all occurrences of with .
Combine and .
Multiply by the reciprocal of the fraction to divide by .
Simplify the expression.
Multiply by .
Rewrite as .
Differentiate using the Power Rule which states that is where .
Combine and .
Multiply by by adding the exponents.
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Subtract from .
Move to the denominator using the negative exponent rule .
Find the Derivative – d/dx log of 1/x