# Directional Derivative

find the directional derivative of z=2x^2-y^3 at (1,1)

is it just <4,-3>

Dick
Homework Helper
That's the gradient. It's not a directional derivative. You can use the gradient to find directional derivatives, but it's not one by itself.

so then how would you go about finding it because where not comparing it with another point.... is it just 1

Dick
Homework Helper
so then how would you go about finding it because where not comparing it with another point.... is it just 1

The directional derivative at (1,1) is the derivative of f(x,y) in some direction. You need to specify the direction to find the directional derivative. Suppose I told you the direction is <u,v>. What's the directional derivative in that direction?

u-1, v-1 and you would dot that with our gradient

we would have to make those unit vector though

Dick
Homework Helper
u-1, v-1 and you would dot that with our gradient

Ok, if (u,v) is a point and you want the directional derivative in the direction which is the difference between (1,1) and (u,v), then sure, it's <u-1,v-1>.<4,-3>. If you are just given the direction <u,v>, I'd say it's <u,v>.<4,-3>. Since they didn't give you a direction I'm not sure what they are asking.

Dick