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 is the probability that |x| < 2 , A number x is chosen at random ...

A number x is chosen at random from the numbers -3, -2, -1, 0 1, 2, 3. What is the probability that  | x| Ans :    x  can take 7 values To get |x| Probability (| x |

Determine how many square centimeters, Determine how many square centimeter...

Determine how many square centimeters of paper are needed to make a label on a cylindrical can 45 cm tall with a circular base having diameter of 20 cm. Leave answer in terms of π.

Determine differential equation from direction field, Thus, just why do we ...

Thus, just why do we care regarding direction fields? Two nice pieces of information are there which can be readily determined from the direction field for a differential equation.

Build an equation for a hyperboloid of two sheets, 1. Build an equation for...

1. Build an equation for a hyperboloid of two sheets with the following properties: a. The central axis of the hyperboloid is the y-axis b. The two sheets are 4 units apart, an

Regrouping, in regrouping if we have abig number in the end what should i d...

in regrouping if we have abig number in the end what should i do?add an number on top of it,please help

Directional derivatives, What are directional derivatives? Explain with two...

What are directional derivatives? Explain with two or more examples..

Differential equations, Find the normalized differential equation which has...

Find the normalized differential equation which has {x, xex} as its fundamental set

Pigeonhole principle, By pigeonhole principle, show that if any five number...

By pigeonhole principle, show that if any five numbers from 1 to 8 are chosen, then two of them will add upto 9.    Answer: Let make four groups of two numbers from 1 to 8 like

How many cubic centimetres of cork dust will be required?, A cylindrical ve...

A cylindrical vessel of diameter 14 cm and height 42 cm is fixed symmetrically inside a similar vessel of diameter 16 cm and height 42 cm. The total space between two vessels is fi

Expected value, Expected Value For taking decisions under conditions of...

Expected Value For taking decisions under conditions of uncertainty, the concept of expected value of a random variable is used. The expected value is the mean of a probability

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