If $f ( x ) = e ^ { x } + x ^ { e } + e ^ { x }$

question 113

Essay

If $f ( x ) = e ^ { x } + x ^ { e } + e ^ { x }$ , what are $f ^ { \prime } ( x )$ and $f ^ { \prime \prime } ( x )$ ?

---

Definitions:

Atomic Open Sentence

A type of statement that contains one or more variables, which makes it capable of being true or false depending on the values of these variables.

Truth-functional Compound

A complex proposition whose truth value depends solely on the truth value of its components, determined by specific truth-functional operators.

Quantifier

A logical term denoting the number of instances an entity, such as 'all', 'some', or 'none'.

Atomic Open Sentence

A type of open sentence in logic that contains no logical connectives and involves variables that can make the sentence true or false depending on their values.