Logarithmic differentiation is a method to differentiate complex expressions that are usually very difficult/tedious to differentiate using other rules by taking the derivative of the natural log of the expressions (both left and right side). It basically goes like this:
1. As the equation shows that the left side equals the right side, you can conclude that the natural log of the left side of the equation equals to the natural log of the right side of the equation.
2. Now, take a derivative of both sides (implicit differentiation)
For the left side of the equation, the derivative of lny = dy/dx * 1/y. If you are not familiar with this, this is an important thing to know. Also, for the right side of the equation, I just used a product rule to get the derivative.
Hi, thank you for your question.
Logarithmic differentiation is a method to differentiate complex expressions that are usually very difficult/tedious to differentiate using other rules by taking the derivative of the natural log of the expressions (both left and right side). It basically goes like this:
1. As the equation shows that the left side equals the right side, you can conclude that the natural log of the left side of the equation equals to the natural log of the right side of the equation.
2. Now, take a derivative of both sides (implicit differentiation)
3. Rearrange the equation for dy/dx.
Does this answer your question?