What is the partial derivative of u with respect to t in the given equation?

Thread starter avinash patha
Start date Feb 4, 2009
Tags

Differentiation Partial Partial differentiation

In summary, partial differentiation is a mathematical concept used in calculus to find the rate of change of a function with respect to one variable while keeping other variables constant. It is important because it allows us to analyze functions in multiple dimensions and is used in various fields of science. Unlike ordinary differentiation, it deals with finding the rate of change of a function with respect to one variable while others are held constant. Partial derivatives are the derivatives of a multivariable function with respect to each of its variables, representing the instantaneous rate of change in a specific direction. Some real-life applications of partial differentiation include solving optimization problems and modeling real-world phenomena in fields such as economics and physics.

Feb 4, 2009

avinash patha

if u(x,t)=ae^-gx sin(nt-gx) where A,g and n are const.,and partial derivative of u w.r.t t=
a^2[(partial derivative w.r.t x(partial derivative of u w.r.t x)] show :(1/a)[n/2]^1/2=g

Physics news on Phys.org

Feb 4, 2009

NoMoreExams

So... show some attempt?

Related to What is the partial derivative of u with respect to t in the given equation?

What is partial differentiation?

Partial differentiation is a mathematical concept used in calculus to find the rate of change of a function with respect to one of its multiple variables, while keeping the other variables constant.

Why is partial differentiation important?

Partial differentiation is important because it allows us to analyze the behavior of a function in multiple dimensions. It is also a crucial tool in many fields of science, including physics, chemistry, and economics.

How is partial differentiation different from ordinary differentiation?

Ordinary differentiation involves finding the rate of change of a function with respect to a single variable. Partial differentiation, on the other hand, deals with finding the rate of change of a function with respect to one variable while keeping all other variables constant.

What is the meaning of partial derivatives?

Partial derivatives are the derivatives of a multivariable function with respect to each of its variables. They represent the instantaneous rate of change of the function in a specific direction.

What are some real-life applications of partial differentiation?

Partial differentiation is used in various fields, such as physics, engineering, economics, and biology, to solve optimization problems and model real-world phenomena. For example, it is used in economics to analyze the relationship between multiple variables, such as supply and demand, and in physics to study the behavior of multivariable systems, such as thermodynamics and electromagnetism.