Potential Energy: Differentiating to Find Force

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omarMihilmy
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Photo of a textbook page showing problem 49: a potential energy function U = 3x^3y - 7x for a two-dimensional force; asks to find the force at (x, y). Problem 50 partially visible below.
Printed textbook answer key showing answers 39 to 51, including the vector expression (7 - 9x^2 y) i-hat minus (3x^3) j-hat for item 49, with energy answers in joules.
To find the force we will differentiate the function with respect to x (dx)
My problem is with the solution
If we differentiate:
dU/dx = 9x^2 - 7

From where does the negative come from also the j component?
 
You should have used the homework template, then you have written the relevant equations. What equation is relevant for finding force from potential energy?
 
Why are you disregarding the y-component when you differentiate?