Exponential functions, Mathematics

Assignment Help:

Exponential Functions : We'll begin by looking at the exponential function,

                                                             f ( x ) = a x

We desire to differentiate this. The power rule which we looked previous section won't work as which required the exponent to be a fixed number & the base to be a variable. That is accurately the opposite from what we've got with this function.  Thus, we're going to have to begin with the definition of the derivative.

698_exponental function.png

Now, the a x is not influenced by the limit as it doesn't have any h's in it and hence is a constant so far as the limit is concerned.  Therefore we can factor this out of the limit. It specified,

2380_exponental function1.png

Now let's notice as well that the limit we've got above is accurately the definition of the derivative  of f ( x ) = a x  at x = 0 , i.e. f ′ (0) .  Thus, the derivative becomes,

                                                 f ′ ( x ) = f ′ (0)a x

 Thus, we are type of stuck.  We have to know the derivative to get the derivative!

There is one value of a that we can deal along with at this point. There are actually a variety of ways to define e. Following are three of them.


Related Discussions:- Exponential functions

KENDE QE MBESHTETEN NE TE NJEJTIN HARK, korda ab e ndan rrethin me qender o...

korda ab e ndan rrethin me qender o ne dy harqe njeri prej tyre eshte sa trefishi i tjetrit gjeni masat e harqeve dhe masat e trekendeshit aob

Dividing, I don''t know how to do the next step like if I had 73 divided by...

I don''t know how to do the next step like if I had 73 divided by 9 wouldn''t 7 go into nine 1 time then you have to do something else but that is the part I don''t understand

Applications of series - differential equations, Series Solutions to Differ...

Series Solutions to Differential Equations Here now that we know how to illustrate function as power series we can now talk about at least some applications of series. There ar

Area and perimeter, if perimeter is 300m length is 100m.find the breadth

if perimeter is 300m length is 100m.find the breadth

How many hours will it take before the cars are 610 miles, Two commuters le...

Two commuters leave the similar city at the same time but travel in opposite directions. One car is traveling at an average speed of 63 miles per hour, and the other car is traveli

Functions, the function g is defined as g:x 7-4x find the number k such tha...

the function g is defined as g:x 7-4x find the number k such that kf(-8)=f- 3/2

Operations and properties, use an expression to write an expression with fi...

use an expression to write an expression with five 3s that has a value of 0

Find the volume of water left in the cylindrical tub, A solid is in the for...

A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 3.5 cm and the height of the cone is 4 cm. The solid is placed in a cylindr

Symmetric and anti-symmetric relation on a set, 1. Let A = {1,2, 3,..., n} ...

1. Let A = {1,2, 3,..., n} (a) How many relations on A are both symmetric and anti-symmetric? (b) If R is a relation on A that is anti-symmetric, what is the maximum number o

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd