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If f=(1,4) at a given point P, a) Calculate the directional derivative of f(x…

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Wize University Calculus 2 Textbook > Multivariable Functions

Gradient and the directional derivative

2 Activities

If ∇f=(1,4)\nabla f=\left(1,4\right) at a given point PP,

a) Calculate the directional derivative of f(x,y)f\left(x,y\right) at point PP in the direction of the vector ⟨5,12⟩\left\langle5,12\right\rangle.

b) Find a unit vector u⃗\vec{u} such that the directional derivative of f(x,y)f\left(x,y\right) at point PP is zero.
More Gradient and the directional derivative Questions:
Practice: Directional Derivative (2)
Calculate Dv⃗f(x, y, z) D_{\vec{v}}f(x,~y,~z)~where f(x, y, z)=9x13z12+y1010 f(x,~y,~z)=9x^{\frac{1}{3}}z^{\frac{1}{2}}+\frac{y^{10}}{\sqrt{10}}~in the direction of v⃗= <−1, 0, 1>.\vec{v}=~<-1,~0,~1>.