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

Please help me solve these Problems step by step, What angle (to the neares...

What angle (to the nearest degree) corresponds to the cos 0.6 or what is cos-1(0.6)? (Note: Use Appendix I) What angle (to the nearest degree) corresponds to the sin 0.6 or what

Probability, an insurance salesman sells policies to 5 men, all of identica...

an insurance salesman sells policies to 5 men, all of identical age in good health. the probability that a man of this particular age will be alive 20 years hence is 2/3.Find the p

Evaluate the diameter of the pizza box, If the area of a small size pizza i...

If the area of a small size pizza is 78.5 in 2 , what size pizza box would required for the small pizza? (Note: Pizza boxes are calculated according to the length of one side.)

Second order differential equation, Write the subsequent 2nd order differen...

Write the subsequent 2nd order differential equation as a system of first order, linear differential equations. 2 y′′ - 5 y′ + y = 0  y (3) = 6  y′ (3) = -1  We can wri

Decimals, which one of the following examples represents a repeating decima...

which one of the following examples represents a repeating decimal? 0.123123,1.111114,0.777777,4.252525?

Give introduction to pythagorean theorem, Give Introduction to Pythagorean ...

Give Introduction to Pythagorean Theorem ? The Pythagorean Theorem says that for any right triangle: a 2 + b 2 = c 2 , where c is the hypotenuse, and a and b are the legs. T

Determine the second derivative of q (t ) = sec (5t ), Determine the secon...

Determine the second derivative for following functions.                             Q (t ) = sec (5t ) Solution : Following is the first derivative.              Q′ (t

Parallelogram, fig angles of a irregular polygons exterior and interior .

fig angles of a irregular polygons exterior and interior .

Explain factor by grouping, Explain Factor by Grouping ? Factoring by g...

Explain Factor by Grouping ? Factoring by grouping is often a good way to factor polynomials of 4 terms or more. (Sometimes it isn't. It doesn't always work. But it's worth try

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