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vivado [14]
3 years ago
14

HELP ME PLEASE ASAP WORK DUE IN AN HOUR PLEASEEE!!!! WILLING TO GIVE ANYTHING

Mathematics
1 answer:
zvonat [6]3 years ago
7 0

50 x 2 = 100

100 x 2 = 200

200 x 2 = 400

400 x 2 = 800

800 x 2 = 1,600

1,600 x 2 = 3,200

3,200 x 2 = 6,400

6,400 x 2 = 12,800

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Compute the directional derivative of the following function at the given point P in the direction of the given vector. Be sure
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Answer:

The directional derivate is given by: D_{u}(x,y) = \frac{6}{\ln{17}\sqrt{10}}

Step-by-step explanation:

The directional derivative at point (x,y) is given by:

D_{u}(x,y) = f_{x}(x,y)*a + f_{y}(x,y)*b

In which a is the x component of the unit vector and b is the y component of the unit vector.

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f_x(x,y) = \frac{6x}{\ln{(2 + 3x^2 + 3y^2)}}

f_x(1,-2) = \frac{6(1)}{\ln{(2 + 3(1)^2 + 3(-2)^2)}} = \frac{6}{\ln{17}}

f_y(x,y) = \frac{6y}{\ln{(2 + 3x^2 + 3y^2)}}

f_y(1,-2) = \frac{6(-2)}{\ln{(2 + 3(1)^2 + 3(-2)^2)}} = -\frac{12}{\ln{17}}

Directional derivative:

D_{u}(x,y) = f_{x}(x,y)*a + f_{y}(x,y)*b

D_{u}(x,y) = \frac{6}{\ln{17}}\times\frac{3}{\sqrt{10}}-\frac{12}{\ln{17}}\times\frac{1}{\sqrt{10}}

D_{u}(x,y) = \frac{18}{\ln{17}\sqrt{10}} - \frac{12}{\ln{17}\sqrt{10}}[tex][tex]D_{u}(x,y) = \frac{6}{\ln{17}\sqrt{10}}

The directional derivate is given by: D_{u}(x,y) = \frac{6}{\ln{17}\sqrt{10}}

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