Find the directional derivatives of the function f(x,y,z)=2x^2 +3y^2 +z^2 at the point p(2,1,3)


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Question Number 187255 by Spillover last updated on 15/Feb/23

$F i n d t h e d i r e c t i o n a l d e r i v a t i v e s o f t h e$ $f u n c t i o n$ $f (x, y, z) = 2 x^{2} + 3 y^{2} + z^{2} a t t h e p o i n t p (2, 1, 3)$
	Answered by MikeH last updated on 15/Feb/23

	$D_{p} (x, y, z) = (p_{x}, p_{y}, p_{z}) ∙ (f_{x}, f_{y}, f_{z})$ $\Rightarrow D_{p} (x, y, z) = 2 (4 x) + 1 (6 y) + 3 (2 z)$ $\Rightarrow D_{p} (x, y, z) = 8 x + 6 y + 6 z$
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