Derivative of Exponential and Logarithmic Function Concept Question

Click For Summary
SUMMARY

The discussion centers on finding the derivative of the function y=9-x using calculus principles. The correct derivative is identified as dy/dx=-9-xln9, with the application of the chain rule and properties of logarithms. Participants emphasize rewriting the function in exponential form, specifically (eln 9)-x, to facilitate differentiation. The conversation highlights the importance of understanding derivative rules and their application in solving similar problems.

PREREQUISITES
  • Understanding of basic calculus concepts, specifically derivatives
  • Familiarity with the chain rule in differentiation
  • Knowledge of logarithmic properties and their application
  • Ability to manipulate exponential functions
NEXT STEPS
  • Study the chain rule in calculus for derivative applications
  • Learn about logarithmic differentiation techniques
  • Explore the properties of exponential functions in calculus
  • Practice solving derivative problems involving logarithmic and exponential functions
USEFUL FOR

Students studying calculus, particularly those tackling derivatives of exponential and logarithmic functions, as well as educators seeking to clarify these concepts for their students.

jacksonpeeble
Gold Member
Messages
118
Reaction score
2

Homework Statement


y=9-x


Homework Equations





The Attempt at a Solution


dy/dx=-9-xln9

We are provided with the answers. I do not understand the concept behind how to get from the question to the solution. What rule(s) are applied? If somebody could solve this single question, or a similar one, in a step-by-step method, I would greatly appreciate it.
 
Physics news on Phys.org
Do you know how to find d/dx(eu)? If so, you can rewrite 9-x as (eln 9)-x and use that derivative formula on it. You'll also want to use the fact that (ar)s = ars.

Welcome back! Haven't heard from you for a while.
 
Thank you, that is very helpful. It makes sense, but it really seems kind of roundabout... ah, well. Calculus...

Thank you! Lately I've either been able to do my homework (or at least I've suffered in silence), although I'm taking AP Physics this year and I've posted some on that forum, and I occasionally try to contribute on the Pre-Calc boards when possible.
 

Similar threads

Derivative of an Nasty Exponential Function
  • · Replies 7 ·
Replies
7
Views
2K
Find Values of Osculating Circle Tangent to a Parabola
  • · Replies 4 ·
Replies
4
Views
2K
Logarithmic derivative question
  • · Replies 9 ·
Replies
9
Views
6K
Calculating 2nd Total Derivative of u w.r.t. t
  • · Replies 28 ·
Replies
28
Views
3K
Fourier transform of exponential function
  • · Replies 3 ·
Replies
3
Views
3K
Logarithmic Regression Question (TI-84 Plus Graphing Calculator)
  • · Replies 4 ·
Replies
4
Views
3K
Integration that leads to logarithm functions problem
  • · Replies 4 ·
Replies
4
Views
2K
Finding the partial derivative from the given information
  • · Replies 2 ·
Replies
2
Views
2K
Simple derivative of exponential function
  • · Replies 3 ·
Replies
3
Views
1K
Calculate this Integral around the Circular Path using Green's Theorem
  • · Replies 3 ·
Replies
3
Views
2K