(Solved): Let \( f(x)=\ln x \) a. Compute \( f^{\prime}(x), f^{\prime \prime}(x), f^{\prime \prime \prime}(x) ...

Let \( f(x)=\ln x \) a. Compute \( f^{\prime}(x), f^{\prime \prime}(x), f^{\prime \prime \prime}(x), f^{(4)}(x) \), and \( f^{(5)}(x) \). b. Determine a formula for \( f^{(n)}(x) \), where \( n \) is any positive integer. a. \( f^{\prime}(x)=, f^{\prime \prime}(x)=, f^{\prime \prime \prime}(x)=, f^{(4)}(x)=\quad \), and \( f^{(5)}(x)= \) Choose the correct answer below. b. Determine a formula for \( f^{(n)}(x) \), where \( n \) is any positive integer. A. \( f^{(n)}(x)=\frac{(-1)^{n}(n-1) !}{x^{n}} \) B. \( f^{(n)}(x)=(-1)^{n-1}(n-1) ! x^{n} \) C. \( f^{(n)}(x)=\frac{(-1)^{n-1}(n-1) !}{x^{n}} \) D. \( f^{(n)}(x)=\frac{(-1)^{n-1}(n-1) !}{x^{n-1}} \)