Multivariable Chain Rule – Proving an equation of partial derivatives – Exercise 6472


Given the differentiable function


Prove the equation

z'_x+ z'_y=1


We will use the chain rule to calculate the partial derivatives of z.

z'_x=\frac{1}{e^x+e^y}\cdot e^x=


z'_y=\frac{1}{e^x+e^y}\cdot e^y=


We will put the partial derivatives in the left side of the equation we need to prove.

z'_x+ z'_y=




We got one as required.

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