- #1
Kirby77
- 2
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any advice on how to sovle this equation would be very much appreciated:
F(x,t)=cos(0.1t)*sin(3t*2x)
dF/dt=?
F(x,t)=cos(0.1t)*sin(3t*2x)
dF/dt=?
Kirby77 said:any advice on how to sovle this equation would be very much appreciated:
F(x,t)=cos(0.1t)*sin(3t*2x)
dF/dt=?
A partial derivative is a mathematical concept used in calculus to measure the rate of change of a multivariable function with respect to one of its variables, while holding the other variables constant.
Partial derivatives are important because they allow us to analyze the behavior of a function with multiple variables, and understand how changes in one variable affect the overall function. This is especially useful in fields such as physics, economics, and engineering.
A partial derivative is denoted by the symbol ∂, which is read as "partial," followed by the variable with respect to which the derivative is taken. For example, the partial derivative of a function f(x,y) with respect to x would be written as ∂f/∂x.
The main difference between a partial derivative and a regular derivative is that a partial derivative considers only one variable, while a regular derivative considers all variables in a function. In other words, a partial derivative is a measure of the change in a function with respect to one variable, while a regular derivative measures the overall change in the function.
To calculate a partial derivative, you must hold all variables except for the one you are taking the derivative with respect to constant, and then use the rules of differentiation to find the derivative. This process is repeated for each variable in the function, resulting in a set of partial derivatives for each variable.