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

Write down the first few terms of the sequences, Write down the first few t...

Write down the first few terms of each of the subsequent sequences. 1. {n+1 / n 2 } ∞ n=1 2. {(-1)n+1 / 2n} ∞ n=0 3. {bn} ∞ n=1, where bn = nth digit of ? So

Mass marketing, is mass marketing completely dead?

is mass marketing completely dead?

Dividing fractions by fractions with drawing.., how do I divide a fraction ...

how do I divide a fraction by a fraction by drawing a picture

Cylinder - three dimensional spaces, Cylinder The below equation is th...

Cylinder The below equation is the common equation of a cylinder. x 2 /a 2 + y 2 /b 2 = 1 This is known as a cylinder whose cross section is an ellipse.  If a = b we

complex number z, For complex number z, the minimum value of |z| + |z - co...

For complex number z, the minimum value of |z| + |z - cosa - i sina|+|z - 2(cosa + i sina )| is..? Solution) |z| + |z-(e^ia)| + |z-2(e^ia)| we see.....oigin , e^ia , 2e^ia ,  f

Geometry, how to do mathematical proofs

how to do mathematical proofs

Nonhomogeneous differential equations, Let's here start thinking regarding ...

Let's here start thinking regarding that how to solve nonhomogeneous differential equations.  A second order, linear non-homogeneous differential equation is as y′′ + p (t) y′ +

Shares and dividend, write a short note on shares and dividend under the fo...

write a short note on shares and dividend under the following heading: shares ,type of shares,face/nominal value of shares.

Power rule, Power rule: d(x n )/dx = nx n-1 There are really three ...

Power rule: d(x n )/dx = nx n-1 There are really three proofs which we can provide here and we are going to suffer all three here therefore you can notice all of them. T

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