+
there u go if that helps u can copy and paste it
I think it’s a im not that sure though
Answer:
x^2y^2 3y^2
Step-by-step explanation:
its a or the first choice
The <em>directional</em> derivative of
at the given point in the direction indicated is
.
<h3>How to calculate the directional derivative of a multivariate function</h3>
The <em>directional</em> derivative is represented by the following formula:
(1)
Where:
- Gradient evaluated at the point
.
- Directional vector.
The gradient of
is calculated below:
(2)
Where
and
are the <em>partial</em> derivatives with respect to
and
, respectively.
If we know that
, then the gradient is:
![\nabla f(r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{s}{1+r^{2}\cdot s^{2}} \\\frac{r}{1+r^{2}\cdot s^{2}}\end{array}\right]](https://tex.z-dn.net/?f=%5Cnabla%20f%28r_%7Bo%7D%2C%20s_%7Bo%7D%29%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Cfrac%7Bs%7D%7B1%2Br%5E%7B2%7D%5Ccdot%20s%5E%7B2%7D%7D%20%5C%5C%5Cfrac%7Br%7D%7B1%2Br%5E%7B2%7D%5Ccdot%20s%5E%7B2%7D%7D%5Cend%7Barray%7D%5Cright%5D)
![\nabla f (r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{3}{1+1^{2}\cdot 3^{2}} \\\frac{1}{1+1^{2}\cdot 3^{2}} \end{array}\right]](https://tex.z-dn.net/?f=%5Cnabla%20f%20%28r_%7Bo%7D%2C%20s_%7Bo%7D%29%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Cfrac%7B3%7D%7B1%2B1%5E%7B2%7D%5Ccdot%203%5E%7B2%7D%7D%20%5C%5C%5Cfrac%7B1%7D%7B1%2B1%5E%7B2%7D%5Ccdot%203%5E%7B2%7D%7D%20%5Cend%7Barray%7D%5Cright%5D)
![\nabla f (r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{3}{10} \\\frac{1}{10} \end{array}\right]](https://tex.z-dn.net/?f=%5Cnabla%20f%20%28r_%7Bo%7D%2C%20s_%7Bo%7D%29%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Cfrac%7B3%7D%7B10%7D%20%5C%5C%5Cfrac%7B1%7D%7B10%7D%20%5Cend%7Barray%7D%5Cright%5D)
If we know that
, then the directional derivative is:
![\nabla_{\vec v} f = \left[\begin{array}{cc}\frac{3}{10} \\\frac{1}{10} \end{array}\right] \cdot \left[\begin{array}{cc}5\\10\end{array}\right]](https://tex.z-dn.net/?f=%5Cnabla_%7B%5Cvec%20v%7D%20f%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Cfrac%7B3%7D%7B10%7D%20%5C%5C%5Cfrac%7B1%7D%7B10%7D%20%5Cend%7Barray%7D%5Cright%5D%20%5Ccdot%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%5C%5C10%5Cend%7Barray%7D%5Cright%5D)

The <em>directional</em> derivative of
at the given point in the direction indicated is
. 
To learn more on directional derivative, we kindly invite to check this verified question: brainly.com/question/9964491
Answer:
D.3
Step-by-step explanation:
We are going to use the Slope Formula --> (y2-y1)/(x2-x1)
(9-3)/(3-1)=6/2=3