Partial Derivatives - Directional Derivatives - Gradient - Scroll down for Videos

Which of the following is in the direction of tangent line to graph of the function [math]z=f\left(x,y\right)[/math] at [math]\left(a,b\right)[/math] in x-direction?

[math]\left\langle0,1,f_y\left(a,b\right)\right\rangle[/math] [math]\left\langle1,0,f_x\left(a,b\right)\right\rangle[/math] [math]\left\langle a,b,f_x\left(a,b\right)\right\rangle[/math]

Directional Derivative is the slope of the tangent line in a direction

In the below GegoGebra Sheet, we created a vector of [b][u]length of the slope[/u][/b] and [b]in the direction of tangent line[/b].; this way the visual effect is optimal. [br]The vector in the sheet is not the directional derivative;[b] its magnitude is equal to the directional derivative.[br][/b][br](1) When direction [math]\vec{u}[/math] is orthogonal to gradient, the directional derivative is zero. [br](2) When [math]\vec{u}[/math] is in the direction of gradient, the directional derivative is highest; the greatest ascent occurs. [br](3) When [math]\vec{u}[/math] is opposite of gradient, the greatest descent occurs.

x and y directions.

Directional Derivative is the slope of the line shown.

Here to make the

Cerrar

Información: Partial Derivatives - Directional Derivatives - Gradient - Scroll down for Videos