Differentiation tricks/shortcuts

In summary, the individual is struggling to understand the concept of treating dA(x)/dx as a fraction rather than an operator. They are specifically questioning how to cancel out the "with respect to" part in equations involving derivatives and are seeking clarification on when it is appropriate to do so. They suggest defining dA as dA/dx to alleviate confusion.
  • #1
Leb
94
0
This is not a specific HW/CW question, just a gap I have and want to fill.
I came from a school in which calculus was only introduced in the last year so I learned only the basics.

Now, I see more and more stuff like taking an expression, say A=B+C and simply making it to a dA=dB+dC. The problem I have is actually understanding why can we simply cancel out the 'with respect to' part ? That is in dA(x)/dx, the dx part.

I think the main question is: When can we treat dA(x)/dx as a fraction rather then an 'operator' (could not come up with a better for d/dx).

Thanks!
 
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  • #2
Because when everything is being nice and friendly you essentially can treat them as single objects.
If you want to rid yourself of confusion define dA = dA/dx then dA=dB+dC is returned to it's former glory.
 

FAQ: Differentiation tricks/shortcuts

1. What is differentiation?

Differentiation is a mathematical process used to find the rate of change of a function with respect to its independent variable. It is also known as taking the derivative of a function.

2. Why are differentiation tricks or shortcuts useful?

Differentiation tricks or shortcuts can save time and effort in solving complex mathematical problems. They can also help in understanding the behavior of a function and its relationship with its variable.

3. What are some common differentiation tricks or shortcuts?

Some common differentiation tricks or shortcuts include the power rule, product rule, quotient rule, and chain rule. These rules provide a faster and more efficient way to find the derivative of a function.

4. Are there any limitations to using differentiation tricks or shortcuts?

While differentiation tricks or shortcuts can be helpful, they may not be applicable to all functions. Some functions may require more advanced techniques or multiple rules to find the derivative.

5. How can I improve my understanding of differentiation tricks or shortcuts?

The best way to improve your understanding of differentiation tricks or shortcuts is through practice. By solving a variety of problems and applying different rules, you can become more familiar with the concept and develop a better intuition for when to use each trick or shortcut.

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