Find gradient at a point and the directional derivative Multivariable calculus

[Nugget3]

Calculate gradient of f
f(x,y)=x^3+2y^3
at point P (1,1)
and the directional derivative at P
in the direction u of the given vector A -> i-j

I tried to attempt this but i honestly don't know where to start. I began to take the partial derivatives of f. I got f'=3x^2dx+6y^2dy, however that answer doesn't seem correct to me.

 

[LCKurtz]

Calculate gradient of f
f(x,y)=x^3+2y^3
at point P (1,1)
and the directional derivative at P
in the direction u of the given vector A -> i-j

I tried to attempt this but i honestly don't know where to start. I began to take the partial derivatives of f. I got f'=3x^2dx+6y^2dy, however that answer doesn't seem correct to me.

What you have calculated is the total differential of f(x,y), which includes both partials $f_x$ and $f_y$. What is the formula for the directional derivative? Show us what happens when you try to calculate it.

 

[hedipaldi]

it is the dot product of the gradient at P with a unit vector in the given direction

 

[LCKurtz]

What you have calculated is the total differential of f(x,y), which includes both partials $f_x$ and $f_y$. What is the formula for the directional derivative? Show us what happens when you try to calculate it.

it is the dot product of the gradient at P with a unit vector in the given direction

You ignored the part I highlighted in red.

 

[hedipaldi]

try to calculate what?don't you need to calculate the directional derivative?

 

[LCKurtz]

try to calculate what?don't you need to calculate the directional derivative?

Yes. You posted a question because you were apparently stuck on the problem. You have now stated that you need to take the gradient at P dotted into a unit vector. So please do it and show us what exactly you are stuck on.