Logarithmic differentiation
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Whenever you're faced with a function with a variable in the exponent, utilize logarithmic differentiation to take the derivative!
Scenario: Evaluate the derivative of the function below.
Notice... we've got x occurring in an exponent! This means we must use logarithmic differentiation!
- 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 derivative of both sides...
...evaluate...
...isolate (dy/dx)...
...and solve for (dy/dx)!
Answer: The derivative of y (a.k.a. (dy/dx) or y') equals y(ln(x) + 1).