To apply the Chain Rule, set as .

The derivative of with respect to is .

Replace all occurrences of with .

Differentiate using the Product Rule which states that is where and .

To apply the Chain Rule, set as .

Differentiate using the Exponential Rule which states that is where =.

Replace all occurrences of with .

Since is constant with respect to , the derivative of with respect to is .

Move to the left of .

Differentiate using the Power Rule which states that is where .

Multiply by .

Differentiate using the Power Rule which states that is where .

Multiply by .

Apply the distributive property.

Combine terms.

Combine and .

Combine and .

Combine and .

Move to the left of .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Combine and .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Reorder terms.

Find the Derivative – d/dx natural log of xe^(-2x)