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

Conscious consumer, I am comparing building a house and buying a house. whi...

I am comparing building a house and buying a house. which one of the option you would choose.

base - 10 block math, there are 5 small cubes and it reads the 5 small cub...

there are 5 small cubes and it reads the 5 small cubes is 1/100, then what is the ONE?

Word problems, if I read 6 hours of spring break how many minutes did ...

if I read 6 hours of spring break how many minutes did read

Find the radius of the inner circle, The area enclosed between two concentr...

The area enclosed between two concentric circles is 770cm 2 . If the radius of the outer circle is 21cm, find the radius of the inner circle. (Ans :14cm) Ans: Π R 2 - Π r 2 =

Ratio , 5:9 and 3:5 then find a:b:c

5:9 and 3:5 then find a:b:c?

Permuation and combination, how many words can be formed from letters of wo...

how many words can be formed from letters of word daughter such that word contain 2vowles and 3consonant

Geometry, How do you solve (17+w)^2 + w^2 = (25+w)^2

How do you solve (17+w)^2 + w^2 = (25+w)^2

Real numbers, how to present root numbers on a number line

how to present root numbers on a number line

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