What is the Derivative of logx(x) in Base x?

  • Context: Undergrad 
  • Thread starter Thread starter Karlisbad
  • Start date Start date
  • Tags Tags
    Derivative
Click For Summary
SUMMARY

The derivative of the function y = logx(x) is established as 0. This conclusion arises from the fact that logx(x) simplifies to 1, as per the logarithmic identity logb(x) = ln(x)/ln(b). Consequently, the derivative of a constant (1) with respect to x is 0, confirming that dy/dx = 0.

PREREQUISITES
  • Understanding of logarithmic functions and their properties
  • Familiarity with the natural logarithm (ln)
  • Basic knowledge of differentiation rules
  • Concept of logarithmic identities
NEXT STEPS
  • Study the properties of logarithmic functions in depth
  • Learn about differentiation techniques for various types of functions
  • Explore the application of logarithmic identities in calculus
  • Investigate the implications of derivatives in real-world scenarios
USEFUL FOR

Students of calculus, mathematics educators, and anyone seeking to deepen their understanding of logarithmic differentiation.

Karlisbad
Messages
127
Reaction score
0
i would need some help to find the derivative of:

[tex]y=log_{x} (x)[/tex] respect to x..:frown: the log is itself in base "x"...:rolleyes: to make the problem harder.
 
Physics news on Phys.org
Hint: [tex]\log_{b}x = \frac{\ln x}{\ln b}[/tex].

Note that I changed the name of the base to b, rather than x.
 
logx(x)=1. Therefore the derivative=0.
 

Similar threads

Undergrad Differentiability of a Multivariable function
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Partial derivatives of the function f(x,y)
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad How to Derive the Taylor Series for log(x)?
  • · Replies 5 ·
Replies
5
Views
17K
Undergrad Partial Derivative of Convolution
  • · Replies 2 ·
Replies
2
Views
3K
Graduate How to take the spatial derivative of quaternions
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Curl operator for time-varying vector
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Why prove Taylor's theorem with p(x)=q(x)−((b−a)^n/(b−x)^n)q(a)?
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad How to Find the Derivative of F = f(x)/f(x+dx)?
  • · Replies 15 ·
Replies
15
Views
2K
High School Some questions while I self-learn Applied Calculus
  • · Replies 49 ·
2
Replies
49
Views
8K
Graduate Partial derivative of composition
  • · Replies 6 ·
Replies
6
Views
2K