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

Probability, An unbiased die is tossed twice .Find the probability of getti...

An unbiased die is tossed twice .Find the probability of getting a 4,5,6 on the first toss and a 1,2,3,4 on the second toss

Explain venn diagrams, Q. Explain Venn diagrams? Ans. Venn diagram...

Q. Explain Venn diagrams? Ans. Venn diagrams, named after the Englishman John Venn, are "area" or "region" diagrams that can be used to help visualize and organize differe

Trigonometric ratios, to difine trigonometric ratios of an angle,is it nece...

to difine trigonometric ratios of an angle,is it necessary that the initial ray of the angle must be positive x-axis?

Rounding, how do you round to the nearest dollars?

how do you round to the nearest dollars?

Find the sum of all natural no. between 101 and 304, Find the sum of all na...

Find the sum of all natural no. between 101 & 304 which are divisible by 3 or 5. Find their sum. Ans:    No let 101 and 304, which are divisible by 3. 102, 105..........

Trigonometry, important trigonometric formulas for class 10th CBSC board

important trigonometric formulas for class 10th CBSC board

Compute the essential matrix and epipolar lines , 1. In Figure there are th...

1. In Figure there are three cameras where the distance between the cameras is B, and all three cameras have the same focal length f. The disparity dL = x0 - xL, while the disparit

Calculate probability, The following table contains some information about...

The following table contains some information about the model used. Assume the probabilities given by the model are those of being a good writer. Variable

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