Check out this Calculus Question and Its Correct Answer - Expert Reviewed!"

  • Thread starter joejo
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In summary, the conversation is about someone asking for feedback on their work and receiving corrections and explanations on their notation and mathematical concepts. The main point of discussion is the use of incorrect notation in the original work and how to properly represent derivatives in mathematical notation. Overall, the conversation is helpful and informative for the person seeking feedback.
  • #1
joejo
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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!
 

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  • #2
anyone please and thank you!
 
  • #3
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
 
  • #4
His notation is wrong (or at least, not consistent with any sort of standard mathematical notation).

[tex]y = f(x) \Longrightarrow \frac{dy}{dx} = \frac{d}{dx} f(x) \neq \frac{dy}{dx}f(x),[/tex]

(unless [itex]f(x)[/itex], and hence [itex]y[/itex], is constant)
 
Last edited:
  • #5
so how is it suppose to be? i don't get you
 
  • #6
On line 2, on the right hand side where you have the fraction dy/dt, tehre should not be a y. It should be

[tex] \frac{d}{dt} (\frac{t-6}{t+6}) [/tex]
 
  • #7
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)
 
  • #8
Look at my last post, then look at your work.

[tex]\frac{dy}{dx}f(x)[/tex]

means that you are multiplying the derivative of [itex]y[/itex] by [itex]f(x)[/itex]. On the other hand,

[tex]\frac{d}{dx}f(x)[/itex]

means that you are taking the derivative of [itex]f(x)[/itex].
 
  • #9
thanks guys..got you
 
  • #10
Also the last line should read "dy/dt = ..." and not "dy/dx = ...".
 

FAQ: Check out this Calculus Question and Its Correct Answer - Expert Reviewed!"

What is Calculus?

Calculus is a branch of mathematics that deals with the study of change and motion. It involves the use of mathematical models and techniques to analyze continuous change and motion.

What are the two main branches of Calculus?

The two main branches of Calculus are Differential Calculus and Integral Calculus. Differential Calculus deals with the study of rates of change and slopes, while Integral Calculus deals with the accumulation of quantities and the area under a curve.

What is the difference between Derivatives and Integrals?

Derivatives and integrals are two fundamental concepts in Calculus. Derivatives are used to calculate the rate of change of a function at a specific point, while integrals are used to find the area under a curve or the accumulation of a quantity over a certain interval.

What are some practical applications of Calculus?

Calculus has a wide range of practical applications in various fields such as physics, engineering, economics, and statistics. It is used to model and analyze complex systems, optimize functions, and make predictions based on data.

How can I improve my understanding of Calculus?

To improve your understanding of Calculus, it is important to practice solving problems and working through examples. It is also helpful to have a strong understanding of algebra and trigonometry, as these are important foundations for Calculus. Seeking help from a tutor or joining a study group can also be beneficial.

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