a. Use the Chain Rule to find the indicated partial derivatives. z = x4 + x2y, x = s + 2t − u, y = stu2; ∂z ∂s ∂z ∂t ∂z ∂u when s = 1, t = 2, u = 3 b. Use the Chain Rule to find the indicated partial derivatives. w = xy + yz + zx, x = r cos(θ), y = r sin(θ), z = rθ; ∂w ∂r ∂w ∂θ when r = 8, θ = pi/2 c. Use the...
3. Given w = x2 + y2, where x = eat and y = (4+t)2, use the chain rule to determine du
(b). Use the chain rule to find aw and as y = 8 cost, z = s sint when s= 1 and t=0 aw at where w = = 22 + y2 + z2, x = st,
Please label each part of your label clearly Consider the following. W = V 81 - 5x2 - 5y2, X = r cos(2), y = r sin(O) (a) Find Ow/ar and ow/80 by using the appropriate Chain Rule. aw ow an = (b) Find Ow/or and Ow/ae by converting w to a function of r and before differentiating. aw dr ow 20 Submit Answer
- 2 (3) (a) (7 points) Let w = I = + +7, y = cos(2), z = 4t. Use the Chain Rule to express or in terms of t. Then evaluate du at t= . (b) (7 points) Let w = 2+2y-42 es cos(3t), y e28sin(3t) and 2 = = 22 2r-y+3z) Use the Chain Rule to express and in terms of s and t. = 2 = ow os 8 åt
Du (b). Use the chain rule to find and y = scost, z = s sint when s = 1 and t=0 Ow at where w= = 22 + y2 + 22, r = st,
Use the Chain Rule to find the indicated partial derivatives. N = 2 + p = u + vw, 4 = V + Uw, r=W + UV; aN N ƏN ., when u = 2, v = 8, W = 9 du' ov'ow ON ON aw Need Help? Read It Watch It Talk to a Tutor Submit Answer Practice Another Version
1(a) Given that f(x,y) = 6x²y3 – cosx + 5y - siny + 10x, establish the fact that, the order in which the mixed partials derivatives are taken is immaterial. AN [2] = (b) (i)Find the continuous function whose Laplace Transform is 3 F(p) AP [7] P(p2+4) (ii) Determine [-*[0-3]2+26] AP [2] (P-3)2 +16 (c) Find the solution of the IVP; 2y" - y' – 3y = 4x+ex y(0)=-1. y'(0) = -2 AN [9]
Consider the following. w = In(x2 + y), x = 2t, y = 5 - t (a) Find af by using the appropriate Chain Rule. (b) Find by converting w to a function of t before differentiating. -/1 POINTS LARCALC11 13.R.054. Differentiate implicitly to find oux x2 = 9 x + y -11 POINTS LARCALC11 13.R.069. Find an equation of the tangent plane to the surface at the given point. z = x2 + y2 + 9, (1, 2, 14)
use the chain rule to find dz/ds and dz/dt. z=arcsin(x-y), x=s^2+t^2, y=2-6st. dz/ds=? dz/dt=?