logarithmic differentiation

[jessicawaybelle]

need help with this question! using log differentiation to find the derivative

 

[Dr.Peterson]

need help with this question! using log differentiation to find the derivative
View attachment 25537

Please show us what help you need! Have you tried doing it? What went wrong?

If you haven't even started, the first step will be to set the expression equal to y, and take the natural log of both sides. Then simplify and differentiate implicitly.

If you don't have good examples, try here: https://tutorial.math.lamar.edu/classes/calci/logdiff.aspx

 

[skeeter]

[MATH]y = x^{1/2} \cdot e^{x^2-x} \cdot (x+1)^{3/2}[/MATH]
[MATH]\log{y} = \dfrac{1}{2}\log{x} + (x^2-x) + \dfrac{3}{2}\log(x+1)[/MATH]
continue ...

 

[skeeter]

Actually, in calculus it's far better to use $\ln$, or $\log_e$ -- whatever you choose to call it! And that is what was intended.

I apologize for using log as base e without stating such ... force of habit.