I'm sorry, but the question you provided seems to be incomplete and a bit confusing.
Firstly, the function F(x) seems to be a function of y, not x. The notation should be F(y) = y^2 + 5y^3.
Secondly, you're asking for the derivative of F(x) with respect to x, which is not possible without knowing the relationship between x and y in the function.
Lastly, the statement "Sin^2 2:y + tg y + ctg 45 = 0" is unclear and doesn't seem to be related to the function F(x) = y^2 + 5*y^3.
If you could provide more information or clarify your question, I would be happy to help further.
I'm sorry, but the question you provided seems to be incomplete and a bit confusing.
Firstly, the function F(x) seems to be a function of y, not x. The notation should be F(y) = y^2 + 5y^3.
Secondly, you're asking for the derivative of F(x) with respect to x, which is not possible without knowing the relationship between x and y in the function.
Lastly, the statement "Sin^2 2:y + tg y + ctg 45 = 0" is unclear and doesn't seem to be related to the function F(x) = y^2 + 5*y^3.
If you could provide more information or clarify your question, I would be happy to help further.