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Find the directional derivative of f(x, y) = (xy)^1/2 at P(6, 6) in the direction from P to Q(9, 2)

Question

Find the directional derivative of f(x, y) = (xy)^1/2

 at P(6, 6) in the direction from P to Q(9, 2)

check_circleAnswer
Step 1

The directional derivative (D.D) of function f at point P in the direction of vector a is given by,

D.D Vf
ap
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D.D Vf ap

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Step 2

Here, the vector a is, vector in the direction from P(6,6) to Q(9,2).

a=(9-6,2-6)= (3.-4)
And,a=3 +4 = 25 = 5
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a=(9-6,2-6)= (3.-4) And,a=3 +4 = 25 = 5

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Step 3

Now, find the value of gradient of f at point P....

of
of
Vf i
j
дх
y
o(y(ay)
+ j-
= i-
дх
= i-
j
2fry
2x
= i-
j
Now,Vf
= i
+ j
216
26
2
1
-+ j
2
1
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of of Vf i j дх y o(y(ay) + j- = i- дх = i- j 2fry 2x = i- j Now,Vf = i + j 216 26 2 1 -+ j 2 1

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Advanced Math

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