- bram , July It, 2014 I (a) If z=f(x,y) welt u=x²-yz and U=xy find the...
(1 point) Use the chain rule to find ow, where u0 = xy + yz,x = d, y = e sin t, z = e cost First the pieces: Now all together: dw = dw dx + dw dy + dw dz is too horrible to di – og det du di + Öz do is too horrible to write down (correctly).
Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 10z) k C is the line segment from (3, 0, -3) to (4, 4, 1) (a) Find a function f such that F = Vf. f(x, y, z) = (b) Use part (a) to evaluate [s vf. dr along the given curve C.
please help with these questions 7. Find fryzx, for f(x, y, z) = 3 + 2?x – xyz + x+y 8. Use the chain rule to calculate that t = 0, if z = sin(xy), x = 1+1, y = 12 + 2t. 9. Use the chain rule to find us at (u, v) = (1,0), when z = xy, x = u +v?, y = x + v.
dz Find when u = 0, v = 2, if z = sin (xy)+xsin (y), x=u2 +2V2, and y= uv. du az = du 1 = 0, V=2 (Simplify your answer.)
5. Let F(x, y, z) = (yz, xz, xy) and define 2 Crin = {(x,y,z) : x2 + y2 = r2, 2 = h} Show that for any r > 0 and h ER, le F. dx = 0 Crih
4. Let f(x, y, z) = rytan'() + z sin(xy), < = wy=v²v, z = ". Find fu and , using the chain rule.
Find... Find if f(x, y, z) = (x2yz6 + xy) 24c-yz (x2yz6 + xy) 4 (12x25 + 1 (22yz6 + xy) 4 (x² 28 + x) (x2y26 + xy)" მu d) af dy 4 (2xyz + y) (x2yz + xy)
(solve) > Implement the boolean function F(x,y,z) = xy + x'y + yz write all the steps and identify the law rule
Consider z-f(x,y)-1-xy cos(xy) at (2,-1/2) variations in x and y respectively. and let ΔΧ and ây represent small a) (i) Compute ΔΖ, given that ΔΧ_ 0.028 and Δy_-0.039. 1 1 6DP Az 5DP ii) Write out an expression for dz in terms of x,y and d, dy. dz= 2 (iii) Compute dz assuming dr_Δι and dy_ây dz- 5DP b) Use the equation of the tangent plane to z at (2,-1/2) to approximate Approximate value = 1 5DP Consider z-f(x,y)-1-xy cos(xy)...
For the functions w = xy + yz + xz, x=u +21, y=u-2v, and zuv, express dw du dw and ar using the chain rule and by expressing w directly in terms of u and v before differentiating. Then evaluate dw du dw and ov at the point (u, v) = اله | العيا dw dw Express and du ov as functions of u and v dw du dw av Evaluate dw and du ow ar at Nim dw du...