The definition of the derivative, Mathematics

Assignment Help:

The Definition of the Derivative : In the previous section we saw that the calculation of the slope of a tangent line, the instantaneous rate of change of a function, and the instantaneous velocity of object at x =a all needed us to calculate the following limit.

1929_derivation.png

We also saw that along with a small change of notation this limit could also be written like this,

1698_derivation1.png

This is such significant limit and it arises in so several places that we give it a name.  We call it a derivative.  Following is the official definition of the derivative.

Definition : The derivative of f ( x ) w.r.t. x is the function f ′ ( x ) and is described as,

996_derivation3.png

Note as well that we replaced all the a's in (1)  along with x's to acknowledge the fact that the derivative is actually a function as well. We frequently "read" f ′ ( x ) as "f prime of x".


Related Discussions:- The definition of the derivative

Compounding and Simple Interest, A painting was purchased 11 years ago for ...

A painting was purchased 11 years ago for $26900. It has just been sold for $78000. Calculate the flat rate of appreciation p.a.

Evaluate the limit, Evaluate the given limit. Solution : It is a ...

Evaluate the given limit. Solution : It is a combination of many of the functions listed above and none of the limited are violated so all we have to do is plug in x = 3

Find the value of given equations in polynomial , If α & ß are the zeroes ...

If α & ß are the zeroes of the polynomial 2x 2 - 4x + 5, then find the value of a.α 2 + ß 2   b. 1/ α + 1/ ß  c. (α - ß) 2 d. 1/α 2 + 1/ß 2    e.  α 3 + ß 3 (Ans:-1, 4/5 ,-6,

Multiply, 37x7= multiply answer it.

37x7= multiply answer it.

Write down a game each for teach maths to children, Write down a game each ...

Write down a game each to teach children i) multiplication, ii) what a circle is, iii) estimation skills. Also say what you expect the child to know before you try to t

The definition of the limit, The Definition of the Limit In this secti...

The Definition of the Limit In this section we will look at the precise, mathematical definition of three types of limits we'll be looking at the precise definition of limits

Mean, Jocelyn has 6 birds, Their mean age is 10. The mode of their ages is ...

Jocelyn has 6 birds, Their mean age is 10. The mode of their ages is 8. What might their ages be? Show your work.

Algebra2;, log6 X + log6 (x-5) = 1

log6 X + log6 (x-5) = 1

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