Question

Find fx(x,y),fy(x,y),fx(1,3) and fy(-2,4)for the given function.if z=(x,y)=3x³y²-x²y³+4x+9

Answer 1

Answer:Partial derivatives of composite functions of the forms z = F (g(x, y)) can be found ... 10(x. 2 y. 3. + sin x). 9. (2xy. 3. + cos x). Similarly, we find the y-derivative by treating x as ... f (x(s, t),y(s, t)) can be found directly with the Chain Rule for one variable if the “outside” function ... x (1) = −4, y (1) = 5, fx(2, 3) = −6, and fy(2, 3) = 7?

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Given function in 2-D as $3x^3y^2-x^2y^3+4x+9$.

Its derivative with respect to x taking y as a constant is given by:

$f_x(x,y) = 9x^2y^2-2xy^3 +4$

Its derivative with respect to y taking x as a constant is given by:

$f_y(x,y) = 6x^3y-3x^2y^2$

Putting x = 1 and y =3 in $f_x(x,y)$ ; we get:

$f_x(1,3) = 81 - 27+4+9= 64$

Putting x= -2 and y =4 in $f_y(x,y)$ ; we get:

$f_y(-2,4) = 6(-2)^3(4)- 3(-2)^2(4)^2 = -192-192 =-384$

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