Author Topic: dy/dx question and differentiable question (Read 1140 times) Tweet Share

TrueTears · « **on:** December 10, 2008, 07:35:02 pm »

if $y=(x+\sqrt{x^2+1})^2$ show $\frac{dy}{dy}= \frac{2y}{\sqrt{x^2+1}}$

And.. also, to test whether a function, $f(x)$ /hybrid function is differentiable at x=a should I test whether 1. The $f ' (x)$ function is continuous at x=a and also 2. Test whether $\lim_{x \to \ a-}f'(x)$ and $\lim_{x \to \ a+}f'(x)$ exist and are equal. If both points are satisfied, then the function/hybrid function is differentiable at x=a. Is this the way to do test for differentiability, or is it wrong?

Collin Li · « **Reply #1 on:** December 10, 2008, 08:52:00 pm »

$y=\left(x+\sqrt{x^2+1}\right)^2$

Using the chain rule:

$\implies \frac{dy}{dx} = 2\left(x+\sqrt{x^2+1}\right)\left(1 + \frac{x}{\sqrt{x^2+1}}\right)$

$= 2\left(x+\sqrt{x^2+1}\right)\left(\frac{\sqrt{x^2+1} + x}{\sqrt{x^2+1}}\right)$

$= \frac{2}{\sqrt{x^2+1}}\left(x+\sqrt{x^2+1}\right)^2$

$= \frac{2y}{\sqrt{x^2+1}}$

hard · « **Reply #2 on:** December 10, 2008, 09:02:02 pm »

Quote from: coblin on December 10, 2008, 08:52:00 pm

$y=\left(x+\sqrt{x^2+1}\right)^2$

Using the chain rule:

$\implies \frac{dy}{dx} = 2\left(x+\sqrt{x^2+1}\right)\left(1 + \frac{x}{\sqrt{x^2+1}}\right)$

$= 2\left(x+\sqrt{x^2+1}\right)\left(\frac{\sqrt{x^2+1} + x}{\sqrt{x^2+1}}\right)$

$= \frac{2}{\sqrt{x^2+1}}\left(x+\sqrt{x^2+1}\right)^2$

$= \frac{2y}{\sqrt{x^2+1}}$

COZZZZZZZAAAAAAAAAAAAAAAAAAA

lacoste · « **Reply #3 on:** December 10, 2008, 09:07:52 pm »

Quote from: hard on December 10, 2008, 09:02:02 pm

Quote from: coblin on December 10, 2008, 08:52:00 pm
$y=\left(x+\sqrt{x^2+1}\right)^2$

Using the chain rule:

$\implies \frac{dy}{dx} = 2\left(x+\sqrt{x^2+1}\right)\left(1 + \frac{x}{\sqrt{x^2+1}}\right)$

$= 2\left(x+\sqrt{x^2+1}\right)\left(\frac{\sqrt{x^2+1} + x}{\sqrt{x^2+1}}\right)$

$= \frac{2}{\sqrt{x^2+1}}\left(x+\sqrt{x^2+1}\right)^2$

$= \frac{2y}{\sqrt{x^2+1}}$
COZZZZZZZAAAAAAAAAAAAAAAAAAA

righteo

TrueTears · « **Reply #4 on:** December 10, 2008, 09:20:36 pm »

ah yes thanks

Search the forums now!

We have moved!

Author Topic: dy/dx question and differentiable question (Read 1140 times) Tweet Share

TrueTears

dy/dx question and differentiable question

Collin Li

Re: dy/dx question and differentiable question

hard

Re: dy/dx question and differentiable question

lacoste

Re: dy/dx question and differentiable question

TrueTears

Re: dy/dx question and differentiable question

Recent Posts

User:
Password: