Write down the Taylor series up to degree of five for:

$\displaystyle cos(x+y)$ about the point $\displaystyle (0,0)$

For doing questions like these. Should I just remember the formula for the Taylor expansion of $\displaystyle f$ about the point $\displaystyle x_0=(x_0,y_0)$

$\displaystyle \displaystyle f(x,y)=f(x_0)+\frac{1}{1!}(f_x(x_0)(x-x_0)+f_y(x_0)(y-y_0))+\frac{1}{2!}(f_{xx}(x_0)(x-x_0)^2+2f_{xy}(x_0)(x-x_0)(y-y_0)+f_{yy}(x_0)(y-y_0)^2)+...$

Let $\displaystyle P=(0,0)$

$\displaystyle f=1$ at $\displaystyle P$

$\displaystyle f_x=-sin(x+y)=0$ at $\displaystyle P$

$\displaystyle f_y=-sin(x+y)=0$ at $\displaystyle P$

$\displaystyle f_xx=-cos(x+y)=-1$ at $\displaystyle P$

$\displaystyle f_yy=-cos(x+y)=-1$ at $\displaystyle P$

$\displaystyle f_xy=-cos(x+y)=-1$ at $\displaystyle P$

$\displaystyle cos(x+y)\approx 1+\frac{1}{1!}(0(x-0)+y(y-0))+\frac{1}{2!}(-1(x-0)^2-2(x-0)(y-0)-1(y-0)^2)$

Is there an easier way of doing these questions?