Derivatives Of Logarithmic Functions

Step 1: First derivative of $%5Clog%20x$ .
The first derivative of $%5Clog%20x$ is: $%5Cfrac%7Bd%7D%7Bdx%7D%20(%5Clog%20x)%20%3D%20%5Cfrac%7B1%7D%7Bx%7D$

Step 2: Second derivative of $%5Clog%20x$ .
The second derivative is the derivative of $%5Cfrac%7B1%7D%7Bx%7D$ : $%5Cfrac%7Bd%5E2%7D%7Bdx%5E2%7D%20(%5Clog%20x)%20%3D%20-%5Cfrac%7B1%7D%7Bx%5E2%7D$

Step 3: Third derivative of $%5Clog%20x$ .
The third derivative is the derivative of $-%5Cfrac%7B1%7D%7Bx%5E2%7D$ : $%5Cfrac%7Bd%5E3%7D%7Bdx%5E3%7D%20(%5Clog%20x)%20%3D%20%5Cfrac%7B2%7D%7Bx%5E3%7D$

Step 4: General form of the $n$ th derivative.
By observing the pattern, the $n$ th derivative of $%5Clog%20x$ is: $%5Cfrac%7Bd%5En%7D%7Bdx%5En%7D%20(%5Clog%20x)%20%3D%20(-1)%5E%7Bn-1%7D%20%5Cfrac%7B(n-1)!%7D%7Bx%5En%7D$

Final Answer: The $n$ th order derivative of $%5Clog%20x$ is: $%5Cboxed%7B(-1)%5E%7Bn-1%7D%20%5Cfrac%7B(n-1)!%7D%7Bx%5En%7D%7D$

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Derivatives Of Logarithmic Functions

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs