$$f(x,y,z)=x^2+\ln(1+y)+e^{yz}$$
Why
$$f^\prime_y=\frac{1}{1+y}$$
and not
$$f^\prime_y=\frac{1}{1+y}+e^{yz}z$$
having in mind that the third addend in $f$ also contains $y$ (which is a real variable, not a constant)?
This is how I would do this:
$$f^\prime_y=0+\frac{1}{1+y}(1+y)\prime+e^{yz}(yz)\prime=\frac{1}{1+y}+e^{yz}(y\prime z+yz\prime)=\frac{1}{1+y}+e^{yz}z,\text{where }x,z=\text{constants}$$
What is it that I do not understand here?