1. Partial Derivatives

Hi all,

my homework questions states "f(x,y)=sin(x-y) at the point (-3,-3)".

• I distributed sin, and obtained sinx-siny
• holding y constant and differentiating with respect to x, i obtain fx(x,y)=cosx
• the derivative of cos(x) is xcos(x), or -3cos(-3)
• holding x constant and differentiating with respect to y, i obtain fy(x,y)=-cosx
• the derivative of -cos(x) is 3 cos(-3)

for some reason, my answers are wrong. I was wondering if someone could help me walk through the steps. Thank you in advance.

2. Originally Posted by newman611
Hi all,

my homework questions states "f(x,y)=sin(x-y) at the point (-3,-3)".

• I distributed sin, and obtained sinx-siny
• holding y constant and differentiating with respect to x, i obtain fx(x,y)=cosx
• the derivative of cos(x) is xcos(x), or -3cos(-3)
• holding x constant and differentiating with respect to y, i obtain fy(x,y)=-cosx
• the derivative of -cos(x) is 3 cos(-3)

for some reason, my answers are wrong. I was wondering if someone could help me walk through the steps. Thank you in advance.
sorry, but $\displaystyle \sin(x-y) \ne \sin{x} - \sin{y}$

$\displaystyle \sin(x-y) = \sin{x}\cos{y} - \cos{x}\sin{y}$