it's not my homework, I just want to find out how to find a directional derivative of an implicit function. I know what is a directional derivative and how to find it when I have a function in normal form (I mean like like z=x^2+y....). $$ xz + yz^2 = 3xy + 3 $$ the point is: $$ P(1,−1) $$ and the direction (vector): $$ u = [1, 1] $$ Could you give me a formula for this? I know how to compute the derivatives of an implicit function as well.
Implicit differentiation (officially, the Implicit Function Theorem if you rewrite your equation as $F(x,y,z)=0$) allows you to compute the gradient of $z=g(x,y)$, and then you use your usual dot product.
LOL that guy wouldn't help you at all, its better if you think of it as like this,
(dz/dx) = -(Fx/Fz) ;this is the standard formula
that is a negative times, the derivative of f wrt x divided by derivative of f wrt to z.
so it would be,
(dz/dx) = -(z+3y)/(x+y*2z)