Derivatives / partial derivatives rule

In summary, if you are taking a partial derivative of an equation with respect to theta_dot, then theta is constant, but you must keep equation in terms of theta in order to find this equation of motion by Lagrangian methods.
  • #1
disb
5
0
When I am taking a partial derivative of an equation with respect to theta_dot, then theta is constant, right?

What if I am taking partial derivative with respect to theta, will theta_dot be constant?

In this case, theta_dot = omega (angular velocity), but I must keep equation in terms of theta in order to find this equation of motion by Lagrangian methods.

Thanks in advanced to anyone that can help me!
 
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  • #2
If you are finding ∂f/∂θ, then everything else other than θ is constant.


so if you had f=θ22+ωθ ⇒∂f/∂θ=2θ+ω
 
  • #3
So how would take partial derivative of:

y = .5*m*(L*theta_dot)^2 + .5*m*g*L*cos(theta)

1) partial y with respect to theta_dot

AND

2) partial y with respect to theta
 
  • #4
disb said:
So how would take partial derivative of:

y = .5*m*(L*theta_dot)^2 + .5*m*g*L*cos(theta)

1) partial y with respect to theta_dotQUOTE]

Well m,g,L and θ would be constants. So the partial derivative of .5*m*g*L*cos(theta) w.r.t. θ(dot) is 0. So differentiate the first term now.
 
  • #5
Ok, and what about part 2 of my question?

"partial y w.r.t. theta" for the first term is..?

Is the first term a constant in this case??
 
  • #6
disb said:
Ok, and what about part 2 of my question?

"partial y w.r.t. theta" for the first term is..?

Is the first term a constant in this case??

Yes. So differentiate the second term.
 
  • #7
nvm, i got it i think... i am just thinking too hard..

if its partial w.r.t theta(dot), then everything (like theta_double_dot or theta) is considered constant except theta(dot)

if partial w.r.t theta(triple dot), then everything is constant except theta(triple dot)

if partial w.r.t. u(double prime), then u(triple prime), u(prime) and everything else except u(double prime) is constant.

right?
 
  • #8
thanks rock,

took me a while to fully understand it and get it sunk in my head,,

i was just thinking to hard
 

1. What is the derivative rule?

The derivative rule is a mathematical formula that is used to calculate the rate of change of a function. It is used to find the slope of a curve at a specific point, which represents the instantaneous rate of change of the function at that point.

2. What is the difference between a derivative and a partial derivative?

A derivative is the rate of change of a single variable function, while a partial derivative is the rate of change of a multivariable function with respect to one of its variables, holding all other variables constant.

3. How do you find the derivative of a function using the derivative rule?

To find the derivative of a function using the derivative rule, you need to apply the rule to the function and simplify the resulting expression. The derivative rule states that the derivative of a function is equal to the limit of the difference quotient as the change in the independent variable approaches zero.

4. What is the chain rule in derivatives?

The chain rule is a derivative rule that is used to find the derivative of a composite function. It states that the derivative of a composite function is equal to the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

5. Why are derivatives and partial derivatives important in science?

Derivatives and partial derivatives are important in science because they allow us to understand how quantities are changing over time or in response to changes in other variables. They are used in many scientific fields, such as physics, economics, and engineering, to analyze and solve problems.

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