Question

Determine the maximum rate of change of the function f at the point p, and in the direction in which it occurs(written as a unit vector). f(x,y) = 7sec(x)*tan(y) P=(pi/4,pi/4)

Answer 1

I know the maximum rate of change is the magnitude of the gradient of f. I think my issue is finding the partial derivatives. For the partial derivative of f wrt x, I got 7sec(x)*tan(x) and for the partial derivative wrt y I got 7sec^2(x)

Answer 2

fx = 2 sec y * sec x * tan x

Answer 3

remember y is a constant in the partial deriv. with respect to x

Answer 4

Oh yeah, my bad. I got rid of the term with the y in it rather than treating it like a constant (such as the 7) and leaving it in there. Thanks!