Q2) Use the chain Rule to find dw\dt of y w = =+2,x = cos²(t), y = sin² (t), z =, at t = 3

Q: Find a function w = ƒ(x, y) whose first partial derivatives are ∂w/∂x = 1 + ex cos y and ∂w/∂y = 2y…

A:

Q: 10

A: Given:

Q: Compute the first-order partial derivatives of the function. z = sinh (4x° y) (Use symbolic notation…

A: since you have posted multiple question which are not interlinked so i have solved first question as…

Q: Find the value of dz at the point (1)1, If the equation 5xy+ z4x -Qy2 =4 %3| defines z as a function…

A: Given 5xy+z4x-2yz=4to determine dzdx  at  (1, 1, 1)

Q: show that 2 = ar²+by ³ and z = ax³ + bx²y + cxy² + dy give 4 same differential rise to the egn.…

A: Introduction: When a multi-variable function is provided, one can for a partial differential…

Q: Find both first partial derivatives. z = exy az ax dz II

A: topic - partial derivatives

Q: Find the approximate solution of the Poisson equation uxx + Uvy = -1, x| < 1, ly| < 1 u = 0 at x =…

A:

Q: Find both first partial derivatives. sinh(5x + 4y) az %3D dz %3D ду

A: Explanation of the answer is as follows

Q: Find both first partial derivatives. z = cos(10xy) dz az ду II

A:

Q: Choose the correct steady-state oscillation of y" + cy' + y = r(t) with C>0 and r(t) = sin(4t) . 4c…

A:

Q: 2. Using Euler's method with N = 8 and 10. dx/dt = 1 + tsin(tx), x(0) = 0

A: Given dxdt=1+tsintx  and x(0)=0 and N=8, N=10

Q: Find the partial derivative at point(u,v)=(-4,0) of w=ln(xa+yb+za),x=uevsin u y=uevcos u, z=uev,…

A:

Q: tany = C secx

A: The question clearly asks us to find the family of orthogonal trajectories of the given family.…

Q: Sketch the direction field of the differential equa tion.Then use it to sketch a solution curve that…

A: Concept: The two expressions connected by equal to be called an equation. The expression on the two…

Q: b) Find if Scosy Vt3 + 5 dt + tany = x -sinx b) Find if S* Vt2 + 5 dt + siny = x – x°cosy dx2

A: Solve by differentiation

Q: 1. Find the total differential of the ff. at (1, -2).

A: The given function is f(x,y)=xy2-3y+2

Q: By using Laplace transform to solve y" + y = e with y (0) y (0) = y" (0) = 0, what would be Laplace…

A:

Q: dx dy 2 + + x + 5y = 4t, dt dt dx dy + 2x + 2y = 2, dt dt x(0) = 3, y(0) = -4. +

A:

Q: What is the integrating factor of (y – cos² x) dx + cos xdy = 0?

A:

Q: Find all the second partial derivatives. f(x, y) = ln(ax+by)

A:

Q: Find the partial derivative. z = sin(2.a*y – 3xy?) az

A:

Q: Suppose that every constant multiple of a solution is also a solution for a first-order differential…

A: It is given that the differential equation dydt=ft,y, where ft,y is continuous on ty plane. Suppose…

Q: Find both first partial derivatives. z = sinh(7x + 16y) az ax az ду

A: From the given problem: z=sinh7x+16y As we know that: The chain rule: fgx'=f'gx·g'x The Power law:…

Q: Consider the direction field of the differential equation dy/dx=xy-8)- 7-9. y 7 YND but do not use…

A: Given dydx=x(y-8)2-6 We know that slope of linear equation id the it's derivative So, m=dydx

Q: Suppose that the partial derivatives of a function ƒ(x, y, z) at points on the helix x = cos t, y =…

A:

Q: Find both first partial derivatives. z = sinh(6x + 19y) dz дх dz ду

A:

Q: What is the differential equation of the orthogonal trajectories of the family of curves y = Cx ? (A…

A:

Q: Find the solutton of followins ordinery differential e quation. yl- 2y' +y

A:

Q: Find dw/ds and aw/at using the appropriate chain rule. Evaluate each partial derivative at given…

A:

Q: Find both first partial derivatives. z = sinh(4x + 8y) az ax az ay II

A:

Q: Sketch the direction field of the differential equa tion.Then use it to sketch a solution curve that…

A: Given Differential equation : y'=x-xy  ,(1,0) dydx=x(1-y) Now we solve the equation by separation of…

Q: Create a slope field of the differential equation dy cos(t) + cos(y) dt and draw solutions…

A:

Q: Give the integrating factor for 3((y^4)+1)dx+4x(y^3)dy=0. (in terms of x)

A:

Q: If z-f (x y): then its total differential can be expressed as * (),中 (). dyds dy + dz O Option 2 O…

A:

Q: Find both first partial derivatives. z = cosh xy2

A: Given: z=cosh xy2 To determine: ∂z∂x&amp; ∂z∂y

Q: d²x dx 5 dt2 2- 3x = -9t2 – 1 - - dt dx When t = 0, x = 1, = 0, find x when t = 2 dy %3D -

A: Please see the below picture for detailed solution.

Q: Find all the second partial derivative T = e-4r cos(0) -4r, Trr 16e 'cos (0) %3D Tre = 4e -4r,…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: v = exy In(x +y)

A:

Q: Evaluate the curve f(x, y) = 0 which passes through the point (0,4) and satisfies the differential…

A:

Q: b) Find if e Vt2 +5 dt + siny = x- xcosy rsinx ycscx

A: According to Leibniz' rule:

Q: Find all the second order partial derivatives of the function : f(x, y) = In 4ry + sin 3ry + e4z-3y

A:

Q: dg Use the Chain Rule to evaluate the partial derivative at the point (r, 0) = (2/2, 7 where g(x, y)…

A:

Q: Create a slope field of the differential equation dy = cos(t) + cos(y) dt and draw solutions…

A: Given: dydt=cos(t)+cos(y) To find: Slope field To sketch: The solutions corresponding to y(0)=0.5,…

Q: Find all the second partial derivatives (including fxy etc.) a) v = sin(2s^2 − t^3)

A: Please see the explanation below

Q: Q10.a) Find rsinx if tnx Jt +5 dt + siny = x – x²cosy

A:

Q: 2. Use the underermined coefficients method to find the goneal Scution of the differential…

A:

Q: Find dy/dt of y=(1+lnx)/1-lnx

A: consider the equation

Q: (b) Find the partial derivative, g where g(x,y)=sin' (2x+y). (c) Given z= In(2x+3y) with x 2s' (t-s)…

A: