# Math Help - grad vector field

can someone please clarify for me what is the difference btw gradient vector field and directional derivative? im new to this topic and am completely lost:'(

thanks so much!

2. Originally Posted by alexandrabel90
can someone please clarify for me what is the difference btw gradient vector field and directional derivative? im new to this topic and am completely lost:'(

thanks so much!
The gradient is a vector: $\nabla f\!\left(x,y,z\right)=\left<\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z}\right>$

The directional derivative is the dot product between your unit vector and the gradient: $\nabla f\!\left(x,y,z\right)\cdot\mathbf{u}$, which is a scalar quantity.

Does this help?