I can't work out what WolframAlpha is doing wrong with this query: https://www.wolframalpha.com/input/?i=derivative+of+%28vector%7B1%2C2%7D+dot+vector%7Bx%2Cx%5E2%7D%29+with+respect+to+x"derivative of (vector{1,2} dot vector{x,x^2}) with respect to x"
It can do the dot product properly on its own: https://www.wolframalpha.com/input/?i=vector%7B1%2C2%7D+dot+vector%7Bx%2Cx%5E2%7D
@christianp This is certainly worth reporting to Wolfram. In the meantime, you could use the syntax of Mathematica for this, e.g. https://www.wolframalpha.com/input/?i=D%5B%7Bx%2C+x%5E2%7D%2C+x%5D or https://www.wolframalpha.com/input/?i=D%5B%7B1%2C+2%7D.%7Bx%2C+x%5E2%7D%2C+x%5D .
@christianp I forgot to add in my previous response that specifying the differentiation variable is often a good idea instead of making Alpha guess, if you prefer natural language input: https://www.wolframalpha.com/input/?i=derivative+with+respect+to+x+of+%7Bx%2C+x%5E2%7D
it looks like it's just ignoring large parts of my query. "derivative of {x,x^2}" produces the same result: https://www.wolframalpha.com/input/?i=derivative+of+%7Bx%2Cx%5E2%7D+
I still can't see how you get from {x,x^2} to x^3+x^2.