Question

Find all the first and second order partial derivatives of f(x,y)=5sin(2x+y)−10cos(x−y).

A. ∂f/∂x=fx=
B. ∂f/∂y=fy=
C. ∂^2f/(∂x^2)=fxx=
D. ∂^2f/(∂y^2)=fyy=
E. ∂^2f/(∂x∂y)=fyx=
F. ∂^2f/∂y∂x=fxy=

Answer 1

$$A. f^{_{x}^{'}}=10cos(2x+y)+10sin(x-y).$$

$B. f^{_{y}^{'}}=5cos(2x+y)-10sin(x-y).$

$C. f^{_{xx}^{''}}=-20sin(2x+y)+10cos(x-y).$

$D. f^{_{yy}^{''}}=-5sin((2x+y)+10cos(x-y).$

$E. f^{_{yx}^{''}}=-10sin(2x+y)-10cos(x-y).$

$F. f^{_{xy}^{''}}=-10sin(2x+y)-10cos(x-y).$