The task is to find following function differential: $$f(x,y)=x^y+y^x.$$ Am I right saying that $$df=(yx^{y-1}+\ln y\cdot y^x)dx+(xy^{x-1}+\ln x \cdot x^y)dy?$$
Not sure about it, as I've missed several lessons on this topic.. Will appreciate any responses
Your solution is entirely correct. For future reference WolframAlpha is entirely capable of finding the same solution, allowing you to quickly verify your own solution. Scroll to the bottom to find the desired answer under the heading 'Differential'.