Office_Shredder said:[tex] g( \lambda _ = f( \lambda x)[/tex]
Then [tex]g'( \lambda ) = \sum_{i=1}^{n} \frac{df}{dx_i} \frac{d( \lambda x}{dx_i}[/tex]
The right hand side is obtained using the chain rule. Try to calculate what the right hand side really is
A partial derivative is a mathematical concept in multivariable calculus that measures the rate of change of a function with respect to one of its variables, while holding all other variables constant.
To calculate a partial derivative, you first need to identify the variable you want to take the derivative with respect to. Then, treat all other variables as constants and use the rules of derivatives to find the derivative of the function with respect to the chosen variable.
The notation for a partial derivative is similar to that of a regular derivative, but with a subscript indicating the variable you are taking the derivative with respect to. For example, ∂f/∂x represents the partial derivative of f with respect to x.
A partial derivative only considers the change in one variable, while holding all other variables constant. A regular derivative considers the change in the entire function with respect to one variable.
Partial derivatives are important in many areas of science and engineering, as they allow us to understand how a function changes when only one variable is changing. They are also used in optimization problems and in the study of functions with multiple variables.