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

What are real numbers, The hole set of irrational and rational numbers is t...

The hole set of irrational and rational numbers is the set of real numbers and is representing by R. Thus, the real numbers can also be describe in terms of position of a point on

Graphical method for interpolation, Graphical Method Whil...

Graphical Method While drawing the graph on a natural scale, the independent variables are marked along the horizontal line and corresponding dependen

Profit, A wholesaler allows a discount of 20% on the list price to a retail...

A wholesaler allows a discount of 20% on the list price to a retailer. The retailer sells at 5% discount on the list price.If a customer paid Rs 114 for an article,what profit is m

Steps for alternating series test, Steps for Alternating Series Test Su...

Steps for Alternating Series Test Suppose that we have a series ∑a n and either a n = (-1) n b n or a n = (-1) n+1 b n where b n > 0 for all n.  Then if,   1.

Iceviga, Jess had a book with 100 pages to read she only read 10 how many p...

Jess had a book with 100 pages to read she only read 10 how many pages does she have to read?

Explain graphing equations with a negative slope, Explain Graphing Equation...

Explain Graphing Equations with a Negative Slope? If the slope is a negative fraction, place the negative sign on either the numerator or the denominator. Example graph y = -2/

Solve:, A Cleaning solution has 40% vinegar. Find the amount of vinegar in ...

A Cleaning solution has 40% vinegar. Find the amount of vinegar in 32 ounces of the solution>

Population problem - nonhomogeneous systems, The next kind of problem seems...

The next kind of problem seems as the population problem. Back in the first order modeling section we looked at several population problems. In such problems we noticed a single po

Solving whole-number riddles, I am greater than 30 and less than 40. The su...

I am greater than 30 and less than 40. The sum of my digits is less than 5. who am I?

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