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

Statistics, How do I choose a distribution test for a sample size of 60? Pr...

How do I choose a distribution test for a sample size of 60? Probability of rolling a 4 on a six sided die.

first person drawn was named the class president, Consider a class of 55 s...

Consider a class of 55 students. The student names are placed in a hat & 3 names are randomly drawn without replacement. a)     If the first person drawn was named the class presi

Utilizes the infinite definition of the limit to prove limit, Utilizes the ...

Utilizes the definition of the limit to prove the given limit. Solution Let M > 0 be any number and we'll have to choose a δ > 0 so that, 1/ x 2   > M

Engg maths, How to get assignment to solve and earn money

How to get assignment to solve and earn money

Ratios, the ratio of boys to girls in the sixth grade is 2:3 if there are ...

the ratio of boys to girls in the sixth grade is 2:3 if there are 24 boys, how many are girls?

Linear approximations, Linear Approximations In this section we will l...

Linear Approximations In this section we will look at an application not of derivatives but of the tangent line to a function. Certainly, to get the tangent line we do have to

What will the day of the week be the further time at the gym, Max goes to t...

Max goes to the gym every fourth day. Ellen's exercise routine is to go every third day. Today is Monday and both Max and Ellen are at the gym. What will the day of the week be the

Fractions, which fractions is equivalent to 5/ 6 a.20/24 b.9/10 c.8/18 d....

which fractions is equivalent to 5/ 6 a.20/24 b.9/10 c.8/18 d.10/15

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