Exponential functions, Mathematics

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.

Posted Date: 4/12/2013 3:13:20 AM | Location : United States

Related Discussions:- Exponential functions, Assignment Help, Ask Question on Exponential functions, Get Answer, Expert's Help, Exponential functions Discussions

Write discussion on Exponential functions
Your posts are moderated
Related Questions
A pool is surrounded through a deck that has the similar width all the way around. The total area of the deck only is 400 square feet. The dimensions of the pool are 18 feet throug

Prove: 1/cos2A+sin2A/cos2A=sinA+cosA/cosA-sinA

In the earlier section we looked at first order differential equations. In this section we will move on to second order differential equations. Just as we did in the previous secti

First, a solution to an equation or inequality is any number that, while plugged into the equation/inequality, will satisfy the equation/inequality. Thus, just what do we mean by

you are driving on a freeway to a tour that is 500 kilometers from your home. after 30 minutes , you pass a freeway exit that you know is 50 kilometer from your home. assuming that

There are only Chinese and Malay pupils in a hall.The ratio of the number of boys to the number of girls is 2:3.The ratio of the number of Chinese boys to the number of Malay boys

find the normalised differential of the following {1,x,x^3}

y= -3x tell if it is linear or not. our teacher wants it graphed or something.

Using the formulas and properties from above find out the value of the subsequent summation. c The first thing that we require to do here is square out the stuff being summe

The price of heating oil rose from $1.10 per gallon to $1.43 per gallon. What is the percent of increase? The price of heating oil rose $0.33 ($1.43 - $1.10 = $0.33). To ?nd ou