Directional derivative of a function \( f\left( x,y\right)\) is represented by \(\delta_{u} f(x, y)\) , where \( \Delta \) is called nabla or also page We should have prior knowledge of partial derivatives and gradients to find directional derivatives. If v is a tangent vector to M at p, then the directional derivative of f along v, denoted variously as df(v) (see Exterior derivative),

v

f
(

p

)

{\displaystyle \nabla _{\mathbf {v} }f(\mathbf {p} )}

(see Covariant derivative),

L

sites
v

f
(

p

)

{\displaystyle L_{\mathbf {v} }f(\mathbf {p} )}

(see Lie derivative), or

v

p

(
f
)

{\displaystyle {\mathbf {v} }_{\mathbf {p} }(f)}

(see Tangent space §Definition via derivations), can be defined as follows. 364 units per length. We’ll also need some notation out of the way to make life easier for us let’s let \(S\) be the level surface given by \(f\left( {x,y,z} \right) = k\) and let \(P = \left( {{x_0},{y_0},{z_0}} \right)\). .

• Previous entry
• Next entry