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

Surds, solve for x: logx9

solve for x: logx9

Linear algrebra, how do we solve multiple optimal solution

how do we solve multiple optimal solution

Quadratic equation, how to solve this? y = 7x - 12 y = x2 Solve the sy...

how to solve this? y = 7x - 12 y = x2 Solve the system using substitution.

Area of a circle, There's a nice way to show why the expresion for the area...

There's a nice way to show why the expresion for the area of a circle of radius R is: Pi * R 2 . It has an comman relationship with the experation for the circumference of a

How to grow your brand with existing customers., "To grow your brand, you n...

"To grow your brand, you need to encourage your existing customers to buy your product a liitle more often. It is far more important to maximise the number of times your buyers buy

Management, An investment manager at TD Ameritrade is making a decision abo...

An investment manager at TD Ameritrade is making a decision about a $10,000,000 investment. There are four portfolio options available and she is looking at annual return of these

Inequalities, seven more than a number is less than or equal to -18

seven more than a number is less than or equal to -18

Regression, A regression line drawn as Y=C+1075x, when x was 2, and y was 2...

A regression line drawn as Y=C+1075x, when x was 2, and y was 239, given that y intercept was 11. calculate the residual

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