If
\[
f(x,y,z,w)=x^{2}e^{2y+3z}\cos(4w),
\]
then
\[
\frac{\partial f}{\partial z}
\]
at \((2,0,-2,1)\) is
Show Hint
For functions of the form
\[
f=x^m e^{ax+by+cz}\sin(kz)
\quad\text{or}\quad
f=x^m e^{ax+by+cz}\cos(kz),
\]
while taking the partial derivative with respect to one variable:
• Treat all other variables as constants.
• Apply the chain rule only to the exponential term.
• Substitute the given point only after obtaining the derivative.
This saves time and reduces calculation errors in competitive examinations.