11.3#9

Dear Dr. Taylor,
I have been working on this problem and I am a little confused why the answers are positive instead of negative. When I took the derivative of the function I got (dz/dx)=-3cos(-3x-5y+z) and (dz/dy)=-5cos(-3x-5y+z). From here I plugged in the point (0,0,0) and received the answer -3,-5.

Thanks

*************************

well, I'm not sure but I guess you're thinking of the equation z = sin(-3x-5y) instead of the equation that's really there. If you think about the real one, you have one equation and three variables, so you can think of one of the variables as a function of the other two--in this case you should think of z = z(x,y).   Then you can find the partial derivatives of both sides of the equation with respect to x and y; the partials of the right hand side are both zero, while the partials of the left side can be  computed using the chain rule--and the part of the chain rule that involves multiplying by the derivatives of the argument will include multiplying by ∂z/∂x or by ∂z/∂y.  (BTW, one follow on effect of this is that it will change the sign of your derivatives.)