Differential calcuals basic first year

You should have 2xy-1-3y^2 = 0. So when you took out dy/dx, you should have dy/dx = (1-2xy)/(x^2-3y^2).
  • #1
obaid
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Homework Statement


find dy/dx x^2 y-x=y^3


Homework Equations


Power rule, Product rule, chain rule, General power rule


The Attempt at a Solution



2xy+x^2 dy/dx -1=3y^2 dy/dx ( took the derivative of both sides)

2xy+x^2 dy/dx -1-3y^2 dy/dx=0 ( Subtracted the right side)

dy/dx(x^2-3y^2)=2xy-1 ( took out dy/dx)

dy/dx=2xy-1 / (x^2-3y^2) ( final answer)


Is this correct?

It looks much nicer on word
 
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  • #2
It would look much nicer in TeX too. But what you have is fine. Your algebra failed you in the third step. You are off by a '-' sign. How did 2xy-1 just move over to the right side?
 

FAQ: Differential calcuals basic first year

What is differential calculus?

Differential calculus is a branch of mathematics that deals with the study of rates of change and how things change over time. It is used to analyze and model continuous systems, such as motion, growth, and decay.

What are the main concepts in differential calculus?

The main concepts in differential calculus include derivatives, limits, and rates of change. Derivatives represent the instantaneous rate of change of a function at a given point, while limits are used to find the behavior of a function at a certain point. Rates of change refer to how a quantity changes over time.

How is differential calculus used in real life?

Differential calculus is used in many fields, such as physics, engineering, economics, and biology. It is used to model and analyze various real-world phenomena, such as the motion of objects, growth and decay of populations, and optimization problems in business and economics.

What are the basic principles of differential calculus?

The basic principles of differential calculus include the power rule, product rule, quotient rule, and chain rule. These rules are used to find the derivative of a function, which is the key concept in differential calculus.

Is differential calculus difficult to learn?

Like any subject, the difficulty of learning differential calculus depends on the individual's background and level of understanding. However, with proper instruction and practice, anyone can learn the basic principles and applications of differential calculus.

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