Proving dy/dx = (a+4b)x^(a+4b-1) for y = x^(2a+3b)/x^(a-b), a and b Integers

Thread starter tofu
Start date Mar 6, 2004
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Calculas

In summary, Calculus is a branch of mathematics that studies change and motion and is used to analyze real-world problems in a precise and systematic way. It is used in various fields such as physics, engineering, economics, and medicine, and has two main branches: differential calculus and integral calculus. Common applications of Calculus include optimization, related rates, and solving differential equations. To improve understanding, regular practice and seeking help from a tutor or study group is recommended.

Mar 6, 2004

tofu

Show that dy/dx = (a+4b)x^(a+4b-1) if y = x^(2a+3b) / x^(a-b) and a and b are integers

thx

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Mar 6, 2004

meteor

If you have
[tex]
y=\frac{fx}{gx}
[/tex]
then
[tex]
\frac{dy}{dx}=\frac{gx*(fx)'-fx*(gx)'}{(gx)^2}
[/tex]

Mar 6, 2004

HallsofIvy

Science Advisor

Homework Helper

Much more simply:
y = x^(2a+3b) / x^(a-b)
= x^((2a+3b)-(a-b))
= x^(a+ 4b)

Now, what is y'?

1. What is Calculus and why is it important?

Calculus is a branch of mathematics that deals with the study of change and motion. It is important because it helps us understand and analyze real-world problems, such as rates of change, optimization, and motion, in a precise and systematic way.

2. How is Calculus used in everyday life?

Calculus is used in various fields such as physics, engineering, economics, and even medicine. It helps in predicting the behavior of physical systems, optimizing production processes, analyzing financial data, and modeling biological processes.

3. 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 study of accumulation and area under curves.

4. What are some common applications of Calculus?

Some common applications of Calculus include optimization problems, related rates, curve sketching, finding areas and volumes, and solving differential equations. It is also used in fields such as computer science, statistics, and data analysis.

5. How can I improve my understanding of Calculus?

To improve your understanding of Calculus, it is important to practice regularly and solve a variety of problems. Additionally, seeking help from a tutor or joining a study group can also be beneficial. It is also helpful to review the fundamental concepts and make connections between different topics in Calculus.