use the chain rule to find dz/dt or dw/dt w=xey/z, x=t2, y=1-t, z=1+2t

Q: Find the Integrating factor of: dy + y. sec5x = tan5x dx 1 (sec5x + tan5x) 5 O sec5х — tanп5x + 5 O…

A:

Q: Determine the function y = eax + b that best fit the data x =(3, 2, 1, 0)T ,y =(µ, 1, e,1/e)T

A: Consider the given information. y=eax+b And, x,y =(3, 2, 1, 0)T ,(µ, 1, e,1e)T=3210,µ1e1e

Q: Show that 1 < arg (z).

A: Inequality - A statement of an order relationship—greater than, greater than or equal to, less…

Q: 1 Selving ou au at

A: We solve it by seperation of variable method.

Q: Calculate fx(l, 3) and /y(l, 3) for f (x, y) =

A: Given: fx,y=7x+y2

Q: Find the gradient of f(m, n) = m³ +n³. grad f = i +

A:

Q: when u = 0, v =1 if du Use Chain Rule to find z = sin ry + x sin y, r= u² + v² and y= uv.

A: Given: z=sinxy+xsiny, x=u2+v2 and y=uv. To find: ∂z∂u at u=0, v=1. Solution: Partial derivative of a…

Q: find the homogenous linear equation of the function y = x2 sinx+ e5x

A:

Q: Determine D,f (4,-1,6) for f(x,y,z) = ery + 4zx in the direction of (-3,2,6).

A: Given fx,y,z=ex2y+4zx3 in the direction of -3,2,6

Q: Determine which of the following pairs of functions are linearly independent. NO_ANSWER 1. f(0) =…

A: The linear dependency of functions can be evaluated using the value of the Wronskian of those…

Q: Find the gradient of w= 3x² - 5y* + 2z at the point (1, 1, -2)

A: The given function is: w=3x2-5y2+2z2

Q: Find the gradient of the curve y = a²xe-b*x at x = 1.

A:

Q: linearise R = AT + BT

A: To linearise the below equation. R=AT+BT2

Q: (4xy) w = 3 sin (4xy tan (z) +4 In (5yz)- 8 e

A:

Q: What is the linear approximation for any generic linear function y=mx+b?

A: Given: y=mx+b

Q: Find the directions of maximum and minimum change of f at the given point, and the values of the…

A: Given :   f(x,y) = 4y2e3x  Point : ( 5,2)