Find D𝔲 f at P. f(x, y, z)=y e^x z+z^2 ; P(0,2,3) ; 𝐮=(2)/(7) 𝐢-(3)/(7) 𝐣+(6)/(7) 𝐤

Name: Problem 6, Chapter 13: Calculus Early Transcendentals
Uploaded: 2020-08-10T02:42:19-08:00
Duration: 1 min 28 s
Channel: Subhadeepta Sahoo
Description: Find D𝔲 f at P. f(x, y, z)=y e^x z+z^2 ; P(0,2,3) ; 𝐮=(2)/(7) 𝐢-(3)/(7) 𝐣+(6)/(7) 𝐤

step 1 In this question F is a function of three variables so we need to find a granite f first which i

Find D𝔲 f at P. f(x, y, z)=y e^x z+z^2 ; P(0,2,3) ;...

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Key Concepts

Dot Product

The dot product is an algebraic operation that takes two equal-length sequences of numbers and returns a single number. It is used to combine the gradient vector and the unit direction vector to calculate the directional derivative by projecting the gradient onto the given direction.

Unit Vector

A unit vector is a vector of length one used to specify direction. In the context of directional derivatives, the direction vector must be a unit vector to ensure that the derivative reflects the true rate of change in that direction.

Gradient

The gradient is a vector that contains all of the partial derivatives of a function. It points in the direction of the steepest ascent and its magnitude represents the maximum rate of increase of the function at a given point.

Directional Derivative

The directional derivative measures the rate at which a function changes at a point in the direction of a given vector. It quantifies how the function increases or decreases as one moves from that point in a specified direction.

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