??=
?? =
?? =
??? =
??? =
??? =
??? =
??? =
??? =
Find all the first and second order. partial derivatives of f(x, y) = 8 sin(2x + y) - 2 cos(x - y). A. SI = fr = B. = fy = c. = f-z = D. = fyy = E. By = fyz = F. = Sxy=
Find the first-order partial derivatives (fr. f,) and second-order partial derivatives (fxxıfyy, fxy, fyx) of the following functions. a. f(x,y)=x’y+x’y? +x+y? b. f(x, y) = (x + y)? Find the critical points at which the following function may be optimized and determine whether at these points the function is maximized, minimized or at a saddle point. z = 5x2 – 3y2 – 30x + 7y + 4xy
(10 points) Find all first and second partial derivatives of f(x,y) = 24 – 3.z”y2 + y* [Note: By Theorem 13.3 on page 913 of the textbook, it should be that fry = fyr:]
Find the limit, if it exists, or show that the limit does not exist. 1. lim (x²y3 – 4y?) (2,y)+(3,2) 2. lim 24 - 4y2 (x,y)+(0,0) x2 + 2y2 3. Find the first partial derivatives of the function of f(x,y) = x4 + 5.cy 4. Find all the second partial derivatives of f(x,y) = x+y + 2.x2y3 5. Find the indicated partial derivatives. f(1, y) = x^y2 – røy ; farzz, fryz
TICKET-IN-THE-DOOR Conceptual: Given a function z = f(x,y), write what the following notations mean in words. • 1x = 2t (partial denotion off wit x • ly =of sportial derivative off wit y) dy • 1. - 2f (2nd partial derivativt off wit > • ly = df (2nd portial derivative off wrt yo Practice: 1. Find the first-order partial derivatives of the following functions a. w -2xy + 5yVx+ 7y5 b. f(x,y) = ek + y Inx 2. Find...
4. (5 points) (a): Find all second partial derivatives of f(x, y) = re-2ry, (b): Find dw/dt at t = 1 if w = re + y sin z - cosz, r= 2/t, y=t-1+ lnt, and 2 = t.
Find all second order partial derivatives of f(x, y) = (x² +3y)
2. Consider the following function: Compute each of the following: Hint: There is probably a better way to compute these than to just mindlessly compute all ot partial derivatives in the order given 3. Is there a function f(x, y) with partial derivatives f, (z, y) = 2r + 5e" + 4y and f,(x, y) = 2y + 5e" + 2x? If so, give an example of a function with these partial derivatives. If not, say why not
2. Consider...
3. Find all second partial derivatives of f(x,y) = ry - 3ry2 + 2y2,2 4. Find and sketch the domain of f(x,y) = . In (?-?-1)
find all first partial derivatives
f(x,y)= 5x^3+4y-3
Find all first partial derivatives. f(x, y) = 5x3 + 4y - 3 f(x,y) = f(x,y) =