The formula for calculating the partial derivative of exp(x+z) is simply exp(x+z) itself. This is because the partial derivative only takes into account one variable, while holding all other variables constant.
To find the partial derivative with respect to x, you simply treat z as a constant and differentiate exp(x) with respect to x. This results in an answer of exp(x).
No, the partial derivative only considers changes in one variable, while the total derivative takes into account changes in all variables. The total derivative of exp(x+z) would be exp(x+z) * (1 + 1) = 2exp(x+z).
Yes, you can use the chain rule to find the partial derivative of exp(x+z) with respect to x. This involves differentiating exp(x+z) with respect to x, and then multiplying by the derivative of x+z with respect to x, which is simply 1.
The partial derivative of exp(x+z) remains constant regardless of the values of x and z, as long as they are held constant while differentiating. This is because exp(x+z) is an exponential function, which has a constant rate of change regardless of the input values.