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

Taylor series, If f(x) is an infinitely differentiable function so the Tayl...

If f(x) is an infinitely differentiable function so the Taylor Series of f(x) about x=x 0 is, Recall that, f (0) (x) = f(x) f (n) (x) = nth derivative of f(x)

Polynomials, On dividing p(X)=5x^(4)-4x^(3)+3x^(2)-2x+1 by g(x)=x^(2)+2 if ...

On dividing p(X)=5x^(4)-4x^(3)+3x^(2)-2x+1 by g(x)=x^(2)+2 if q(x)=ax^(2)+bx+c, find a,b and c.

Define period, Q. Define Period, Amplitude and Phase Shift? Ans. P...

Q. Define Period, Amplitude and Phase Shift? Ans. Period, amplitude and phase shift are used when describing a sinusoidal curve The period of a function is the smallest

Calculate the density of people per square mile, 1.  In 1900, a certain cou...

1.  In 1900, a certain country's population was 77,977,459 and it's area was 2,821,924 square miles, In 2000, the country's population was 283,575,229 and its area was 3,551,003 sq

Example of developing an understanding, In class 1, the teacher had written...

In class 1, the teacher had written down the digits 0,1, ...., 9 on the board. Then she made all the children recite the corresponding number names. Finally, she made them write th

Calculus, I need help with my calculus

I need help with my calculus

Factor expressions involving large powers, Factor Expressions Involving Lar...

Factor Expressions Involving Large Powers, Radicals, and Trig Functions You can use substitution to factor expressions involving large powers, radicals, and trig functions

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