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

Advanced functions, writ the equation that describes the motion of a point ...

writ the equation that describes the motion of a point on the wheel that has a center of 4m off the ground, has radius of 15 cm, makes a full rotation every 10 seconds and starts a

Mathematical model representing the total parking cost, John has a choice o...

John has a choice of using one of two parking garages when he visits downtown: Option1:  $8 an hour for the first two hours, then $2 and hour for each hour more than 2; or Op

Simultaneous equations by substitution, Simultaneous equations by substitut...

Simultaneous equations by substitution: Solve the subsequent simultaneous equations by substitution. 3x + 4y = 6      5x + 3y = -1 Solution: Solve for x: 3x = 6

Factor Fiction, Ok this is true or false wit a definition. The GCF of a pai...

Ok this is true or false wit a definition. The GCF of a pair of numbers can never be equal to one of the numbers.

Calculate the slope of the line, Calculate the slope of the line: Exa...

Calculate the slope of the line: Example: calculate  the  slope  of  the  line  whose  equation  is  y  =  2x  +  3  and  whose y-intercept is (0,3). Solution:    y =

Stat, defination of uper boundarie .

defination of uper boundarie .

How i get orders, how i become an assignment helper?n how i get order from ...

how i become an assignment helper?n how i get order from students?what should i do

Linear Equations, Tommy has a Nexus 4 that charges poorly. He placed his ph...

Tommy has a Nexus 4 that charges poorly. He placed his phone to charge,after 20 minutes the phone was 27% and after 85 minutes the phone was at 66%. Find how many percentage the p

Adding integers, Do you subtract when you add integers.

Do you subtract when you add integers.

Trignometry, Prove that cosec2theta+ sec2theta can never be less than 2

Prove that cosec2theta+ sec2theta can never be less than 2

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