Find the derivative of a function ln x x .
Find the derivative of a function .
Answer & Explanation
The quotient rule states that:
where the apostrophe means "the derivative of".
In this example, we let and
This allows us to rewrite the function as:
Other calculus rules tell us that the derivative of is always . As a result, the first half of our numerator becomes , Which neatly simplifies to . This gives:
Now we can use the power rule, which states that . Since we know that nn in this case is (because has no exponent), this becomes , which yields a value of . This gives us our final answer: