# Directional derivative tangent to a curve

1. Nov 27, 2011

### MeMoses

1. The problem statement, all variables and given/known data

Given xz^2-yz+cos(xy)=2 which defines z implicitly in terms of x and y, find the directional derivative of z in the direction of the tangent to the curve y=x^2+2x-1 at the point (0,1) in the direction of decreasing x

2. Relevant equations

3. The attempt at a solution
I'm fairly positive I just take the negative of the gradient of z multiplied by the unit vector of the tangent of the curve, all at the point. I have the gradient of z but what is the unit vector of the tangent? I think the tangent would be 2x+2 but I know it has to be divided by something to be a unit vector. This is where my notes become inconsistent and I'm not sure what to do

2. Nov 27, 2011

### vela

Staff Emeritus
If you draw in the tangent vector to the curve, you should be able to see that $\tan \theta = dy/dx$, where $\theta$ is the angle the vector makes with the horizontal axis.

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