Move the negative in front of the fraction.

To apply the Chain Rule, set as .

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

Replace all occurrences of with .

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

Rewrite as .

Differentiate using the Power Rule which states that is where .

Multiply.

Multiply by .

Multiply by .

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

Simplify the expression.

Multiply by .

Add and .

Rewrite the expression using the negative exponent rule .

Combine and .

Find the Derivative f(x)=e^(-1/x)