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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.
Give the Introduction to Scientific Notation? In mathematics, it can be very difficult and time-consuming to do calculations involving very large and very small numbers. This i
give me the derivation of external division of sectional formula using vectors
3x^2+19x-14=0
A compound fraction is a fraction that has other fractions inside its numerator or denominator. Here's an example: While compound fractions can look really hairy, they're r
A right triangle whose sides are 15 cm and 20 cm is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Ans : 3768cu.cm,1318.8
In an election contested between A and B, A obtained votes equal to twice the no. of persons on the electoral roll who did not cast their votes & this later number was equal to twi
Fundamental Theorem of Calculus, Part II Assume f ( x ) is a continuous function on [a,b] and also assume that F ( x ) is any anti- derivative for f ( x ) . Then,
how to do it
how many times In a 12 hour period will he numbers add up to 6? (hint 3:00 is one answer0
Differentials : In this section we will introduce a notation. We will also look at an application of this new notation. Given a function y = f ( x ) we call dy & dx differen
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