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 .

Multiply by .

Rewrite as .

Differentiate using the Power Rule which states that is where .

Combine and .

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