Question

If f(x)=ln(7xln(x)), what is f ′(1)?

A) 1/7
B) 1/e
C) ln(7)
D) 0

Answer 1

To find f'(1), we need to find the derivative of the function f(x) = ln(7xln(x)) using the chain rule. After finding the derivative, we substitute x = 1 to find f'(1), which turns out to be undefined.

Step-by-step explanation:

To find the derivative of the function f(x) = ln(7xln(x)), we can use the chain rule. Let's start by rewriting the function as f(x) = ln(7) + ln(x) + ln(ln(x)). Now, let's find the derivative of each term:

• derivative of ln(7) is 0, since it's a constant
• derivative of ln(x) is 1/x
• derivative of ln(ln(x)) is 1/(xln(x))

Now, we can add all the derivatives together: f'(x) = 0 + 1/x + 1/(xln(x))

To find f'(1), we substitute x = 1 into the derivative: f'(1) = 0 + 1/1 + 1/(1ln(1)) = 1 + 1/0 = undefined