Finding the second order partial derivative of a function: z = ln (e ^ x + e ^ y)? When finding the first order derivative of X, why does the answer e ^ x become When we get the first derivative of X, why does the answer e ^ x become a molecule?

Finding the second order partial derivative of a function: z = ln (e ^ x + e ^ y)? When finding the first order derivative of X, why does the answer e ^ x become When we get the first derivative of X, why does the answer e ^ x become a molecule?

Let f (x, y) = e ^ x + e ^ y
Original title: Z (x, y) = ln f (x, y) = ln (e ^ x + e ^ y) this is the problem of finding the derivative of a composite function. To find the partial derivative of Z to x, we first find the derivative of the logarithmic function ln (), because the derivative of LN x is 1 / x, so the whole of e ^ x + e ^ y goes to the denominator, and then we find the derivative of F (x, y) to X. at this time, e ^ y is treated as a constant
∂z/∂x = e^x/(e^x+e^y) （1）
∂z/∂y = e^y/(e^x+e^y) （2）
The second partial derivative is used to (1) and (2) to find the second derivative for X and Y respectively