91影视

Use the definition of the partial derivative to find the partial derivatives specified in Exercises 23鈥�26.

$f_y\left(2,1\right)$when localid="1650225390806" $f\left(x,y\right)=9-x^2-y^2$.

In Exercises 21鈥�26, (a) determine whether the given subset of $R^2$is open, closed, both open and closed, or neither open nor closed, (b) find the complement of the set, and (c) find the boundary of the given set.

All the points satisfying the inequality $\left|x\right|+\left|y\right|鈮�1$

Partial derivatives: Find all first- and second-order partial derivatives for the following functions:

$f(x,y,z)=x{z}^2{e}^y$

In Exercises $21鈥�28$, find the directional derivative of the given

function at the specified point$P$ and in the direction of the

given unit vector$u.$

$f(x,y)=\frac{x}{y^2}\text{at}P=(鈭�2,1),\mathbf{u}=\left\{\frac{\sqrt{10}}{10},鈭�\frac{3\sqrt{10}}{10}\right.>$

In Exercise, evaluate the given function at the specified points in the domain, and then find the domain and range of the function.

$g\left(x,y\right)=\frac{x^2+y^2}{x+y},\left(\mathrm{蟺},1\right),\left(4,5\right)$

In Exercises 21鈥�26, (a) determine whether the given subset of $R^2$is open, closed, both open and closed, or neither open nor closed, (b) find the complement of the set, and (c) find the boundary of the given set.

All points $(x,y)$such that $\left|x\right|<1$and $\left|y\right|鈮�2$

In Exercises 21-28, find the directional derivative of the given function at the specified point \(P\) and in the direction of the given unit vector \(\mathbf{u}\).

Use the definition of the partial derivative to find the partial derivatives specified in Exercises 23鈥�26.

$f_x\left(0,-3\right)\text{and}{f}_y\left(0,-3\right)\text{when}f\left(x,y\right)=\frac{3x}{y^2}$

In Exercises $21-28$, find the directional derivative of the given

function at the specified point $P$and in the direction of the

given unit vector $u$.

localid="1650380514741" $f(x,y)=\frac{x}{y^2}\text{at}P=(鈭�2,1),\mathbf{u}=鈭�\frac{5}{13}\mathbf{i}+\frac{12}{13}\mathbf{j}$

Partial derivatives: Find all first- and second-order partial derivatives for the following functions:

$f(x,y,z)=\ln 鈦�(x+y+z)$