Find the indicated partial derivative. $$f ( x , y ) = x ^ { 2 } y ^ { 4 } - 3 x ^ { 4 } y , f _ { m x }$$
A) $f _ { xx x } = 12 x ^ { 2 } y$
B) $f _ { xx x } = - 36 x y$
C) $f _ { xx x } = 3 x y$
D) $f _ { xxx } = - 72 x y$
E) $f _ { xx x } = - 3 x y$

Question

Find the indicated partial derivative. $$f ( x , y ) = x ^ { 2 } y ^ { 4 } - 3 x ^ { 4 } y , f _ { m x }$$
A) $f _ { xx x } = 12 x ^ { 2 } y$
B) $f _ { xx x } = - 36 x y$
C) $f _ { xx x } = 3 x y$
D) $f _ { xxx } = - 72 x y$
E) $f _ { xx x } = - 3 x y$

Quizplus · Accepted Answer

Taking the partial derivative of $f$ with respect to $x$ gives: $\frac{\partial}{\partial x}f(x,y)=2xy^4-12x^3y.$ Then taking the partial derivative of this with respect to $x$ gives: $\frac{\partial ^2}{\partial x^2}f(x,y)=2y^4-36x^2y,$ and finally, taking the partial derivative of this with respect to $x$ gives: $\frac{\partial ^3}{\partial x^3}f(x,y)=-72xy.$ Therefore, $f_{xxx}=-72xy.$

Find the Indicated Partial Derivative f(x,y)=x2y4−3x4y,fmxf ( x , y ) = x ^ { 2 } y ^ { 4 } - 3 x ^ { 4 } y , f _ { m x }f(x,y)=x2y4−3x4y,fmx​

Find the Indicated Partial Derivative $f ( x , y ) = x ^ { 2 } y ^ { 4 } - 3 x ^ { 4 } y , f _ { m x }$