Question of differentiation

In summary, differentiation is a mathematical concept used to find the rate of change of a function. It is important in science as it helps us understand relationships between variables and solve problems. Differentiation is the inverse operation of integration and is used in real-life applications such as calculating speed and growth rates. There are various methods of differentiation, including the power, product, quotient, and chain rules. These methods make the process more efficient and allow us to find derivatives of different types of functions.
  • #1
yungman
5,718
241
I am confuse with this:

[tex]Let\;\; t=jx \;\;,\;\; j =\sqrt{-1}[/tex]

[tex] \Rightarrow \frac{dt}{dx}=j[/tex]

But if I use [tex]t^2=-x^2 \;\Rightarrow\; 2t\frac{dt}{dx}=-2x[/tex]

[tex]\Rightarrow \frac{dt}{dx}=-\frac{x}{t}[/tex]

What is wrong?
 
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  • #2
sub back t=jx, and then multiply by j/j
 
  • #3
rock.freak667 said:
sub back t=jx, and then multiply by j/j

Nice!

Thanks
 

1. What is differentiation?

Differentiation is a mathematical concept that refers to the process of finding the rate of change of a function. It involves calculating the slope of a curve at a specific point.

2. Why is differentiation important in science?

Differentiation is important in science because it allows us to analyze and understand the relationship between variables in a system. It also helps us to make predictions and solve problems in various fields such as physics, biology, and economics.

3. What is the difference between differentiation and integration?

Differentiation and integration are inverse operations. Differentiation is the process of finding the rate of change, while integration is the process of finding the original function from its rate of change. They are both important in mathematical modeling and problem solving.

4. How is differentiation used in real life?

Differentiation is used in many real-life applications, such as calculating the speed of an object in motion, determining the growth rate of a population, and finding the optimal solution in business and economics.

5. What are the different methods of differentiation?

There are several methods of differentiation, including the power rule, product rule, quotient rule, and chain rule. These methods allow us to find the derivative of various types of functions and make the process of differentiation more efficient.

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