Question
Asked Nov 3, 2019

Eavluate the gradient vector at the given point.

a) f(x,y) = cos2(πxy) at (1,-1)

b) f(x,y,z) = xeyz at (2,1,0)

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Expert Answer

Step 1

a) Given function is 

f(x, y) cos (Txy)
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f(x, y) cos (Txy)

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Step 2

Firstly, we find partial derivatives of f with respest to x and y

s(х.у) —- 2лусos(тху)sin(тxy)
S (х, у) --2тхсos(тху)sin (тху)
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s(х.у) —- 2лусos(тху)sin(тxy) S (х, у) --2тхсos(тху)sin (тху)

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Step 3

Now, gradient vector of f(x,y) at...

У(х,у) - 1.(х.у)і +s, (х,y)j
V(х.у) -- 2лусos (тху)sin (тxу)i - 2лх сos (тху)sin (тху) j
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У(х,у) - 1.(х.у)і +s, (х,y)j V(х.у) -- 2лусos (тху)sin (тxу)i - 2лх сos (тху)sin (тху) j

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Tagged in

Math

Calculus

Derivative