Imagine you were faced with a function like this:
We've never dealt with a variable in the exponent! How can we solve for the derivative when we're faced with this?
Whenever you're faced with a function with a variable in the exponent, utilize logarithmic differentiation to take the derivative!
How to solve with logarithmic differentiation
The procedure for logarithmic differentiation is the following:
- Take the natural log (ln) of both side of your function
- Simplify your expression as much as possible
- Go through implicit differentiation steps
Take the natural log (ln) of both side of your function
This step is pretty easy: simply surround both sides of the equation with a natural log (ln)!
Simplify your expression as much as possible
For this step, we're going to rely on the following log property:
How does this apply to our equation?