Question

Let f (x comma y )equals 4 x squared minus 9 x y plus 6 y cubed. Find f subscript x (x comma y ).

Answer 1

Fx(x,y) = 8x -9y

Explanation:

Given f(x,y) = 4x²-9xy+6y³, we are to find the derivative of the function with respect to x keeping y as constant.

Fx(x,y)

This is known as partial derivative of the function.

Fx(x,y) = 2(4)x^(2-1) - 9y + 0

Fx(x,y) = 8x -9y

Note that the differential of a constant is zero, hence the reason why 6y³ tends to zero since there are no x variable attached.