Doug_West said:Homework Statement
Let f be a differentiable function of one variable, and let
z = f(x + 2y). Show that
2∂z/∂x − ∂z/∂y = 0
Homework Equations
Multi-variable chain rule
The Attempt at a Solution
I have no idea where to start with this, any advice would be greatly appreciated.
Thanks in advance,
Doug
Doug_West said:would it be f'(g(x,y))*1?
The Multivariable Chain Rule is a mathematical concept that is used to find the derivatives of functions with multiple variables. It states that the derivative of a composition of two or more functions is equal to the product of the derivatives of those functions.
The Multivariable Chain Rule is used when a function has multiple independent variables and is composed of multiple functions. It is commonly used in multivariable calculus and in physics and engineering applications.
To apply the Multivariable Chain Rule, you must first identify the composite function and then take the derivative of each individual function. Finally, you multiply the derivatives together to find the overall derivative.
The Multivariable Chain Rule is used to find the derivatives of functions with multiple variables, while the Single Variable Chain Rule is used for functions with only one variable. The Multivariable Chain Rule involves taking partial derivatives, while the Single Variable Chain Rule involves taking ordinary derivatives.
Yes, there are some special cases where the Multivariable Chain Rule may not apply, such as when the function is not differentiable or when there are discontinuities in the function. It is important to check the assumptions and conditions of the rule before applying it to a particular function.