iv.y %3D cot1 (x), у € [0, п] v.y = sec-1 (x), y e |-1, – u|0, vi. y = csc=1 (x) , y € [-T, – U [0. 2

Q: (a) By using thẻ chain rülé and the dérivative (1, (1xl) = {"1, if x>0 if x<0' d %3D dx 1-1, find -…

A:

Q: (x – cos y)dx – sin ydy = 0 Of (x, y) = -xe-# +e-* cos y + k (y) ;f (r, y) = -e- sin y dy +k (y) Of…

A:

Q: a. Around the point (1,0), is f(x.y) = x (y+ 1) more sensitive to changes in x or to changes in y?…

A: Solution

Q: Find the external in the isoperimetric problem of the extremum of subject to f(y² +xy'- :“)dx= 2,y…

A: Consider the functional  Iyx=∫x1x2Fx,y,y'dxwith the conditions yx1=y1 , yx2=y2and Iyx=∫x1x2Gx,y,y'dx…

Q: 3. y" +2y' + y = 2 sin t H(t – n), y(0) = 1, y'(0) = 0 A y(t) = (t+1)e-[cost+ (t+1-)e™-']H(t–n) %3D

A: The given differential equation is: y''+2y'+y=2 sin(t) H(t-π) ;              y(0)=1,   y'(0)=0

Q: Find partial derivative føyz of the function f(x, Y, z) = z ln x + 2y

A:

Q: Find both first partial derivatives. h(x, y) = e-(x° + y9) h,(x, y) = %3D h,(x, y) = %D

A:

Q: 1. Find the total derivative dz/dy, given (a) z = f(x, y) = 5x + xy - y2, where x = g(y) = 3y² (b)…

A:

Q: Let y = tan(2z + 3). Find the differential dy when z = 2 and dæ = 0.4 Find the differential dy when…

A:

Q: lim r.y)→(0,0) (4 + (x² + y²) In(x² + y?)) Dose not exist -00 00 1 4-

A:

Q: Find the indicated partial derivative. f(x, y, z)=euz²; fzyz fxyz(x, y, z) =

A:

Q: (a) z = x2 + y² + xy, x = sin t, y = e'. (b) z = x2 + y², x = cos t + sin t, y = cost – sin t. %3D

A:

Q: Compute the partial derivative of the function f(r, y, z) = e'-z cos(y) + z e=1/(1+y²) vith respect…

A:

Q: Q4) Ir z-y,Determine the first order partial derivative (w.r.t, x) and (w.r.t, y)

A:

Q: Let y=5x^2Find the change in y, Δy when x=3 and Δx=0.2Find the differential dy when x=3 and dx=0.2

A: To find the following parts. 1.)find the change in y (∆y), when x=3 and ∆x=0.2. 2.)find the…

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = tanh (x + 2y + 3z)

A: We have given fx,y,z=tanhx+2y+3z and we have to calculate fx,fy and fz

Q: Given the function f(x,y) cos 2xーx3eY +āyン COS find te second partial olerivative fxy.

A: Let f(x,y) is the given function.Then  fx is the derivative of f with respect to x taking y as a…

Q: 2x,x X, +X, Find the total differential dy, given

A: Introduction: On an open set S, let z=f(x,y) be continuous. Changes in x and y are represented by dx…

Q: w =sec (xyz) - Yx +y+z

A:

Q: (1) Use the Chain Rule to find dz/dt. (a) z = r² + y² + xy, r= sint, y = e'. z = x2 +y?, x = cost+…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: = y – 2², dt dy = y - ar. - у — dt For parameter a, classify the equilibrium points when a>5

A: Both the equilibrium points (0, 0) and (a, a2) are saddles.   Explanation: Let   First, we find the…

Q: 36. Using the approximation dy dy h dr * Yn+1- y. and that dr 1, y = 2 when r 0. Then, y A h- 2 h+ 2…

A: Please see the answer below.

Q: 3) To find the partial derivative of f (x. y) with respect to y at the point (xy. we A)…

A: Solving the question with an example

Q: Let y= tanx .(a) Find the differential dy .(b) Evaluate  dy and ∆y if x= and π /4 and dx =-0.1.

A: Given function is (a) Differentiating with respect to x, we get

Q: of Let f (x,y)=tanh-1(x-y) with x=e" and y= usinh (t). Then the value of evaluated at the point dt…

A:

Q: 22. u- Vr? + s, r- y + x cos 1, s -x+ y sin t; ди ди ди when x= 1, y = 2, 1 = 0 ar ay at

A: Given: u=r2+s2  r=y+x cos t and  s=x+y sin t By using Chain Rule we have to find: ∂u∂x, ∂u∂y ,and…

Q: I the function z(x, y) = ex sin(3y) and x = ut-t², y = √u² + t², Find : dz dz and 2- (by chain rule)…

A:

Q: Integrate f(x,y) = x-5y over the curve C: x +y = 64 in the first quadrant from (0,8) to (V32,/32).…

A: Formula Used:Line integral ∫Cf(x, y) ds=∫abf(x(t), y(t)) dxdt2+dydt2dt

Q: Let y = tan x. (a) Find the differential dy. (b) Evaluate dy and Δy if x = π/3 and dx = -0.2…

A: Let,  y=fanxa To find differential dy, differentiate y       with respect to x,        dy=sec2x dx

Q: For the three variables function u(x, y,z) = (log4 x²) csch¬1(yz)) a3u Evaluate the partial…

A: solution is given below in the Image please follow it

Q: *Yx = cos°(t), y = sin (1),z =, dw = 1 dt w =-+2,x= z Z ==, at t = 3 Ans. t=3

A: Given query is to find derivative of w with respect to t.

Q: 3. Find dy where; (x+y) =2 o) cos(xy)- 주+ ers + b) e+ u= xlax (use chain rule)

A: We have to find the derivative

Q: 22. Find when t=, where x a(t + sint), y= a(I-cost) and a is a constant %3D

A:

Q: Find both first partial derivatives. h(x, y) = e-(x° + y9) h,(x, y) = %3D h,(x, y) = %3|

A:

Q: ution of yl = x+xy2 W

A:

Q: 1 The partial derivative of f(x, y, z) = Arctan with respect to z is xy? z³

A:

Q: dz calculate the partial derivatives dz and ду y? 2. For z = = ln 2 |

A: The solution is given as

Q: Let y=3sqrt(x) Find the change in y, Δy when x=2 and Δx=0.3 Find the differential dy when x=2 and…

A: We are going to solve

Q: 2x lerivatives from first principle, find the derivatives of y = 5 V3x-e2x-(xln x)(In(In x)) -2e2x)…

A: We have to find the derivative from the given function

Q: For the three variables function: u(x, y, z) = [cosh-(x?). cot-(yz)] a3u Evaluate the Partial…

A: We have to find out the partial derivative of given function

Q: approximation of I = [" f(x)dx using composite Simpson's rule with n=4 is:

A: In this question, we evaluate the definite integral by using the composite Simpson's rule for n=4.

Q: E valuate dt + seck tan x dX

A:

Q: an f (b) For a positive integer n, find the n-th partial " azn derivative off with respect to z, for…

A: Solved below.

Q: Let y'=sinxy and y(0)=2 Approximate y(4) using Euler's method with step sizes of .25

A: The solution of a differential equation is defined as the function that satisfies the differential…

Q: Hw #4 ( 2 xy +y -tany) dx+(x²-x tany tSeiy )dy =o ??

A: according to our guidelines we can answer only three subparts, or question and rest can be reposted.…

Q: (a) Find the first partial derivative of (i) f (x, y, z) = x?y %3D z3 (ii) f(x, y, z) = evz cos xy…

A:

Q: 3. Find dy, where; (x+y) = 2 a) cos (xy)- + e b) e+ iPtany=1 , u= xlax (use chain rule)

A:

Q: (b) Find the partial derivative at point (u,v) = (-4,0) of w = In(xª + yß + zª),x = ue"sinu, y =…

A: Chain rule:  Suppose that  are differentiable functions of and  is a differentiable function of .…

Q: Let y=3sqrt(x)Find the change in y, Δy when x=5 and Δx=0.2 Find the differential dy when x=5 and…

A: Given function is Change in y is calculated as follows. when x=5 and Δx=0.2