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.

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,

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.

Posted Date: 4/12/2013 3:13:20 AM | Location : United States

Ask an Expert

Related Discussions:- Exponential functions, Assignment Help, Ask Question on Exponential functions, Get Answer, Expert's Help, Exponential functions Discussions

Write discussion on Exponential functions
Your posts are moderated

Write your message here..

Related Questions

Normal distribution to approximate binomial distribution, Survey 83% of com... Survey 83% of community for a park. Randomly select 21 people if they do or do not want a park. Can you use normal distribution to approximate binomial distribution?If so find mean

#triple integrals, #triple integral of x^2+y^2+z^2 over 0 #triple integral of x^2+y^2+z^2 over 0

Calculate the value of the following limits, Calculate the value of the fol... Calculate the value of the following limits. Solution To remind us what this function such as following the graph. hence, we can see that if we reside to the r

Choose a business organisation which you are familiar with a, help me on th... help me on thus subject pls

Real numbers, prove root 2 as irrational number prove root 2 as irrational number

Percentage, of all those survey 390 were under 18 years of age if 20%were 1... of all those survey 390 were under 18 years of age if 20%were 18, how many responded to the survey

Solve 2 ln (x) - ln (1 - x ) = 2 single logarithm, Solve 2 ln (√x) - ln (1 ... Solve 2 ln (√x) - ln (1 - x ) = 2 . Solution: Firstly get the two logarithms combined in a single logarithm. 2 ln (√x) - ln (x  - l) = 2 ln ((√x) 2 ) ln (1 - x ) = 2

Postage stamp problem, Explain Postage Stamp Problem solving tehcnique? Wha... Explain Postage Stamp Problem solving tehcnique? What is Postage Stamp Problem?

Solving ratios, you are in charge of making punch for an upcoming dance. th... you are in charge of making punch for an upcoming dance. the punch recipe makes 5 cups of punch by making 3 cups of cranberry juice with 2 cups of apple juice. What is the ratio of

Mathematics is all around us-mathematics- in our lives, Mathematics Is All ... Mathematics Is All Around Us :  What is the first thing you do when you get up? Make yourself a nice cup of tea or coffee? If so, then you're using mathematics! Do you agree? Cons