Q4: Find the derivative of the function at P。 in thedirection of A21)_ƒ(x, y)=2xy− 3y², P. (5,5), A = 4i +3j2)g(x,y)=x-(y²/x)+√3 sec¹(2xy), P. (1,1), A=12i+5jf (x, y, z) = xy + yz + xz, P. (1,−1,2), A = 3i+ 6j − 2k3)4) g(x, y, z)=3e* cos(yz), P(0,0,0), A=2i+j−2k

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Answered: Q4: Find the derivative of the function…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. Find the derivative of f(x, y, z) = x³ – xy2 – z at Po(1,1,0) in the direction of V = 2ỉ – 3j + 6k. In what direction does f(x, y, z) change most rapidly at Po and what are the rates of change in these directions?
Compute the partial derivative fxxyz for f(x, y, z) = cos(cos(x3 + z2 )) + x2 ln(y2 + z2 ).
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Demonstrate the use of the method with reflections on the use of numerical methods, find the minimum for the function below: F(x,y)= Ax^2 - Bxy- cy^2= x -y (Xo=4, Yo=4) A=2 B=-2 C=1 Identify the minimum again using the Newton’s method with dynamic . However, use this time numerical derivatives instead of . When using numerical derivatives, only one of the constants is being varied as with partial derivatives. Apply in this case the forward numerical derivative, . Here equals some very small number. For each step , solve first the and optimal using the condition . When taking the derivative of , please remember to consider the inner derivatives for each of the coordinate axes that results as dot product with the main function. In this work it is enough that only the second term in the dot product is analyzed using numerical derivatives. Thus, the function takes the form .

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Q4: Find the derivative of the function at P, in the direction of A 2 1) f(x, y) = 2xy-3y², P. (5,5), A=4i+3j 2) g(x,y)=x-(y²/x)+ √√3 sec¹(2xy). P(1,1), A=12i+5j f(x, y, z)= xy + yz + xz, P(1,-1,2), A = 3i+6j-2k 3) 4) g(x, y, z)=3e* cos(yz), P (0,0,0), A=2i+j−2k