This is not quite the correct partial derivative of T with respect to x. That's the terminology that is usually used.killersanta said:Homework Statement
T(x, y, z) = 200e^(−x^2−3y^2−9z^2 )
I'm not sure how to get the derivative in terms of x,y or z.
The Attempt at a Solution
For x: -200x^2e^(−x^2−3y^2−9z^2 )(-2x)? Is this right? Probably not, how do i do it?
Mark44 said:Do you understand why that x2 factor you had shouldn't be there?
A derivative is a mathematical concept that represents the rate of change of a function with respect to one of its variables. It is essentially the slope of the tangent line to a curve at a specific point.
Taking the derivative of a function allows us to analyze its behavior and understand how it changes. It is also useful in finding the maximum and minimum values of a function, as well as the points where the function is increasing or decreasing.
The derivative of a function can be calculated using several methods, such as the power rule, product rule, chain rule, and quotient rule. It involves finding the derivative of each term in the function and combining them using these rules.
The notation for a derivative is f'(x) or dy/dx, which represents the derivative of the function f with respect to the variable x. It can also be written as d/dx[f(x)].
The derivative of a multivariable function, such as T(x, y, z), is a vector that represents the rate of change of the function with respect to each of its variables. It can be calculated using partial derivatives, which involve taking the derivative of the function with respect to one variable while holding the others constant.