Question

Помогите найти производную

Answer 1

Ответ:

$z=2x^2+y^3\ \ ,\ \ \ M(\ 1\ ;-2\ )\ \ ,\ \ \vec{a}=\{\ 3\ ;-4\ \}\\\\\\z'_{x}=4x\ \ ,\ \ z'_{x}\Big|_{M}=4\cdot 1=4\\\\z'_{y}=3y^2\ \ ,\ \ z'_{y}\Big|_{M}=3\cdot (-2)^2=3\cdot 4=12\\\\\\|\vec{a}|=\sqrt{3^2+4^2}=5\ \ ,\ \ \ \vec{a}^{0}=\Big\{\ \dfrac{3}{5}\ ;-\dfrac{4}{5}\ \Big\} \\\\\\\dfrac{\partial z}{\partial \vec{a}}=4\cdot \dfrac{3}{5}-12\cdot \dfrac{4}{5}=\dfrac{12-48}{5}=-\dfrac{36}{5}=-7,2$