Is my calculus answer correct?

[joejo]

hi,

Below i have attched both my question and answer. Can someone please take a look and tell me if its right? Thanks in advance!

 

[joejo]

anyone please and thank you!

 

[Delta]

Looks absolutely fine to me. Good work.

A bit weird that there is a t on the top and bottom at the start though.

Interesting method of notation too. I always used write in extra u's and v's for the quotient differential, etc. but you've kept it in y's and t's

 

[Data]

His notation is wrong (or at least, not consistent with any sort of standard mathematical notation).

$$y = f(x) \Longrightarrow \frac{dy}{dx} = \frac{d}{dx} f(x) \neq \frac{dy}{dx}f(x),$$

(unless $f(x)$, and hence $y$, is constant)

 

[joejo]

so how is it suppose to be? i don't get you

 

[whozum]

On line 2, on the right hand side where you have the fraction dy/dt, tehre should not be a y. It should be

$$\frac{d}{dt} (\frac{t-6}{t+6})$$

 

[whozum]

You did it more than once,

dy/dt implies the derivative of th eoriginal function, which isn't what your doing in every step, you are taking a derivative of a single term inthe function, hence (d/dt) not (dy/dt)

 

[Data]

Look at my last post, then look at your work.

$$\frac{dy}{dx}f(x)$$

means that you are multiplying the derivative of $y$ by $f(x)$. On the other hand,

[tex]\frac{d}{dx}f(x)[/itex]<br /> <br /> means that you are taking the derivative <i>of</i> $f(x)$.[/tex]

 

[joejo]

thanks guys..got you

 

[neutrino]

Also the last line should read "dy/dt = ..." and not "dy/dx = ...".