# derivative \$f(z,y) = g(x+y)h(y)\$ with respect to \$y\$

Suppose I have differentiable function $$g(x+y)$$ and $$h(y)$$ and define $$z = x+y$$. Also, I assume that for any $$x_1,y_1$$ there exists $$x_2,y_2$$ such that $$g(x_1+y_1) = g(x_2+y_2)$$. Then, I want to take derivate of $$f(z,y) = g(x+y)h(y)$$ with respect to $$y$$ and obtain the result like $$g(x+y)h'(y).$$ I want to know if it is possible. My argument is that whenever I change $$y$$, I can always find $$x’$$ to offset the effect of the change in $$y$$ on function $$g$$.