Interpretations of derivatives, Mathematics

Assignment Help:

Interpretations of derivatives.

Example:   Find out the equation of the tangent line to

                                      x2 + y 2  =9

at the point (2, √5 ) .

Solution

We have to be given both the x & the y values of the point.  Notice that this point does lie on the graph of the circle (you can verify by plugging the points into the equation) and thus it's okay to talk regarding the tangent line at this point.

Recall that to write the tangent line we required is the slope of the tangent line and it is nothing more than the derivative evaluated at the specified point. 

Then the tangent line is.

                                      y =     √5 - 2/ √5  ( x - 2)

Now, let's work on some more examples. 

There is a simple way to remember how to do the chain rule in these problems.  Really the chain rule tells us to differentiate the function as usually we would, except we have to add on a derivative of the inside function.  In implicit differentiation it means that every time we are differentiating a term along y in it the inside function is the y and we will have to add a  y′ onto the term as that will be the derivative of the inside function. Let's see a couple of examples.


Related Discussions:- Interpretations of derivatives

Calculate the probability, Calculate the Probability A bag contains 80...

Calculate the Probability A bag contains 80 balls of such 20 are red, 25 are blue and 35 are white.  A ball is picked at random what is the probability that the ball picked is

Initial conditions to find system of equations, Solve the subsequent IVP. ...

Solve the subsequent IVP. y′′ + 11y′ + 24 y = 0 y (0) =0  y′ (0)=-7  Solution The characteristic equation is as r 2 +11r + 24 = 0 ( r + 8) ( r + 3) = 0

Replacement problems, how we will use the replacement problmes in our life?...

how we will use the replacement problmes in our life?

Class 10, chapter permutation & combination ex :4.6

chapter permutation & combination ex :4.6

????????, ?????? ?????? ?? ???? ??????? ???????? ?????? 3.5 ?? ??? ???? ???...

?????? ?????? ?? ???? ??????? ???????? ?????? 3.5 ?? ??? ???? ???? ????? 50??/???? ??????20??/???? ???? ?? ?? ?????? ???????? ??? ??? ?? ??????? ??????? ? ?? ????? ????

#title.algebra., how do i understand algebra? whats the formula i just dont...

how do i understand algebra? whats the formula i just dont get it

.fractions, what is the difference between North America''s part of the tot...

what is the difference between North America''s part of the total population and Africa''s part

Word problem, A computer is programmed to scan the digits of the counting n...

A computer is programmed to scan the digits of the counting numbers.For example,if it scans 1 2 3 4 5 6 7 8 9 10 11 12 13 then it has scanned 17 digits all together. If the comput

Classify linear or nonlinear, Question: Classify the following differen...

Question: Classify the following differential equations as linear/nonlinear. Also, what is the order of the following differential equations? Xy'-2y =x Xy'' -2y' =xsin(y)

Derivatives, Derivatives The rate of change in the value of a...

Derivatives The rate of change in the value of a function is useful to study the behavior of a function. This change in y for a unit change in x is

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