Simple partial differentiation

Thread starter kasse
Start date May 17, 2008
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Differentiation Partial Partial differentiation

In summary, Simple partial differentiation is a method used in calculus to find the instantaneous rate of change of a function with respect to one of its variables. It is useful for analyzing how changes in one variable affect the overall behavior of a function and is commonly used in physics and engineering. The main difference between simple partial differentiation and total differentiation is that simple partial differentiation involves taking the derivative of a function with respect to one variable, while total differentiation involves taking the derivative with respect to all variables simultaneously. Some common applications of simple partial differentiation include modeling relationships between multiple variables and solving optimization problems. The chain rule in simple partial differentiation states that the derivative of a composite function is equal to the product of the derivative of the outer function and the derivative of the inner

May 17, 2008

kasse

Homework Statement

Differentiate f = arctan(u/v) with respect to u

The Attempt at a Solution

Using the chain rule

f_u = (1/(1 + (u/v)²)) * 1/v = 1/(v + u²/v)

The solutions manual says v/(u² + v²)

What is my mistake?

Physics news on Phys.org

May 17, 2008

hotcommodity

Multiply the top and bottom of your answer by "v" and see what you get

Related to Simple partial differentiation

What is simple partial differentiation?

Simple partial differentiation is a method used in calculus to find the instantaneous rate of change of a function with respect to one of its variables. It involves taking the derivative of a function with respect to one variable while keeping the other variables constant.

Why is simple partial differentiation useful?

Simple partial differentiation is useful because it allows us to analyze how changes in one variable affect the overall behavior of a function. It is commonly used in physics and engineering to model the relationship between multiple variables.

What is the difference between simple partial differentiation and total differentiation?

The main difference between simple partial differentiation and total differentiation is that simple partial differentiation involves taking the derivative of a function with respect to one variable, while total differentiation involves taking the derivative with respect to all variables simultaneously. Total differentiation is used to find the total rate of change of a function, while simple partial differentiation is used to find the rate of change with respect to a specific variable.

What are some common applications of simple partial differentiation?

Simple partial differentiation is commonly used in economics, physics, engineering, and other fields to model relationships between multiple variables. It can also be used to optimize functions and solve optimization problems.

What is the chain rule in simple partial differentiation?

The chain rule in simple partial differentiation states that the derivative of a composite function is equal to the product of the derivative of the outer function and the derivative of the inner function. This rule is used when taking the derivative of a function with multiple variables that are not directly related to each other.