Question

Determine all second order partial derivatives for f(x y) ln 3xy3​

Answer 1

Answer:

f(X)=3

Step-by-step explanation:

this determination All .....

Answer 2

Answer:

All the second order partial derivatives for $f(x,y)=3xy^{3}$ are $f_{xx}=0$, $f_{yx}=9y^{2}$ and $f_{yy}=18xy$.

Step-by-step explanation:

Given: $f(x,y)=3xy^{3}$ ...... (1)

Differentiate function (1) with respect to $x$ (Assume $y$ as constant).

$f_{x}=3y^{3}$ ...... (2)

Differentiate function (1) with respect to $y$ (Assume $x$ as constant).

$f_{y}=9xy^{2}$ ...... (3)

Now, differentiate derivative (2) and (3) with respect to $x$ (Assume $y$ as constant).

$f_{xx}=0$

$f_{yx}=9y^{2}$

Also, differentiate derivative (2) and (3) with respect to $y$ (Assume $x$ as constant).

$f_{xy}=9y^{2}$

$f_{yy}=18xy$

Observe that $f_{xy}=f_{yx}=9y^{2}$.

Therefore, the second order partial derivatives for $f(x,y)=3xy^{3}$ are $f_{xx}=0$, $f_{yx}=9y^{2}$ and $f_{yy}=18xy$.