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 are logarithmic function, The logarithm of a provided number b to the ...

The logarithm of a provided number b to the base 'a' is the exponent showing the power to which the base 'a' have to be raised to get the number b. This number is defined as log a

Finding length and height with volume and width?, I figured out the volume ...

I figured out the volume and the width, but I have no idea how to use that information to get the height and the length!

Dividing using compatible numbers, 4 friends have 235 marbles and want to s...

4 friends have 235 marbles and want to share.How many marbles should each friend receive?

Theorem to computer the integral, Use green's theorem to computer the integ...

Use green's theorem to computer the integral F . dr where F = ( y^2 + x, y^2 + y) and c is bounded below the curve y= - cos(x),, above by y = sin(x) to the left by x=0 and to the r

Matric, fgdg ggghfr hhrhfrf hfrrg jhj hjgg dear friend ghr tu vgu jyyiu ui ...

fgdg ggghfr hhrhfrf hfrrg jhj hjgg dear friend ghr tu vgu jyyiu ui u huik bgyuiiyts husk

Calculate the time average of kinetic energy of the planet, (1) If the coef...

(1) If the coefficient of friction between a box and the bed of a truck is m , What is the maximum acceleration with which the truck can climb a hill, making an angle q with the ho

Solid mensuration, The two sides of a triangle are 17 cm and 28 cm long, an...

The two sides of a triangle are 17 cm and 28 cm long, and the length of the median drawn to the third side is equal to 19.5 cm. Find the distance from an endpoint of this median to

Application of linear function, four times an unknown number is equal to tw...

four times an unknown number is equal to twice the sum of five and that unknown number

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