Consider the following: $$\mathrm{d}U=\frac{\partial U(x,y)}{\partial x}\mathrm{d}x+\frac{\partial U(x,y)}{\partial y}\mathrm{d}y.$$ My question: How is this expression supposed to be understood? The expression above is obviously a measure of the sensitivity to change of the function $U$ but with respect to what?

If needed, more context can be provided.

Consider the following: $$\mathrm{d}U=\frac{\partial U(x,y)}{\partial x}\mathrm{d}x+\frac{\partial U(x,y)}{\partial y}\mathrm{d}y.$$ My question: How is this expression supposed to be understood? The expression above is obviously a measure of the sensitivity to change of the function $U$ but with respect to what?

If needed, more context can be provided.

Some context: This is an expression I encountered when reading about indifference curves. See this wiki link.

Consider the following: $$\mathrm{d}U=\frac{\partial U(x,y)}{\partial x}\mathrm{d}x+\frac{\partial U(x,y)}{\partial y}\mathrm{d}y.$$ My question: How is this expression supposed to be understood? The expression above is obviously a measure of the sensitivity to change of the function $U$ but with respect to what?

Consider the following: $$\mathrm{d}U=\frac{\partial U(x,y)}{\partial x}\mathrm{d}x+\frac{\partial U(x,y)}{\partial y}\mathrm{d}y.$$ My question: How is this expression supposed to be understood? The expression above is obviously a measure of the sensitivity to change of the function $U$ but with respect to what?

If needed, more context can be provided.