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

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

Differentiate using the Power Rule.

Differentiate using the Power Rule which states that is where .

Simplify the expression.

Multiply by .

Reorder terms.

By the Sum Rule, the derivative of with respect to is .

Evaluate .

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

Differentiate using the Power Rule which states that is where .

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

Multiply by .

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

Simplify.

Add and .

Reorder terms.

By the Sum Rule, the derivative of with respect to is .

Evaluate .

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

Differentiate using the Power Rule which states that is where .

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

Multiply by .

Evaluate .

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

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

Simplify.

Add and .

Reorder terms.

By the Sum Rule, the derivative of with respect to is .

Evaluate .

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

Differentiate using the Power Rule which states that is where .

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

Multiply by .

Evaluate .

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

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

Simplify.

Add and .

Reorder terms.

Find the 3rd Derivative xe^x