9. Find for each of the given functions using the chain rule. dx a. y = (4x + 3)3 b. y = v6 + x2 - (4+x3)2

Q: Compute the values of dy and Ay for the function y= e4z + 5z given z = 0 and Az = dz = 0.02.

A: Given x = 0, dx = ∆x = 0.02            (1) Here y = f(x) = e4x+5x

Q: +5t, y=s - 5t, z = st² d aw/ot by using the appropriate Chain Rule. d aw/at by converting w to a…

A:

Q: Consider the following. w = x - ¹₁ x = e³t, y = t³ (a) Find dw/dt by using the appropriate Chain…

A:

Q: Given f (x) = x³+ 5, let L(x) be the linearization based at 2. Find L(2)

A: Given,          The function is fx=x3+5 and the linearization based at 2.

Q: Let g(x,y)=ye-3x, x(t) =ln(t2+1), and y(t) =√t Find g(x(t), y(t))

A: To find: The value of gxt,yt. Given: The functions are gx,y=ye-3x, xt=lnt2+1 and yt=t. Concept used:…

Q: Evaluate the given function using homogeneous x- yArctan () dx + xArctan () dy = 0 A. 2yArctan ()…

A: We need to find solution of differential equation using homogenous.

Q: Q12- Suppose that we, x= 3r+s, y= 3r-s, z= r²s Use appropriate forms of the chain rule to find dw dw…

A: To evaluate by using the appropriate form of the chain rule.

Q: Please help

A: Let,

Q: Find values of C1 and C2 so that the given functions will satisfy the prescribed initial conditions…

A: A detailed solution is given below.

Q: Find dwdt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before…

A:

Q: 14.11 Let f(x, y) = 3xy² + 2x where x(t) -312 and y(t) = 4t3 + t. %3| || %3| a) Use the Chain Rule…

A:

Q: Compute dy if y = x2+x and x changes from x = 2 to x = 2.01.

A:

Q: 35. Give linearly independent functions that are annihilated by D² (D² – 2D + 10).

A: We will find roots for the equation and use concept of differential equations to find the linearly…

Q: (a) It is possible to have E(XY)=E(X)E(Y) when X and Y are not independent.

A: We know that if the Karl Pearson correlation theory, If X & Y are independent then we say that…

Q: 3. Find the linearization L(x) of the function at a. F(x) = Vx, a = 4

A: Use the formula for the linearization of a function about any point.

Q: Suppose z is a function of x and y, and csc Vr² + yz = z"esin. Solve for dz and

A: A multivariable function is a rule that connects two or more variables. The partial derivative of a…

Q: 7. Let f(x, y) = 10xy* + x°y². Find fyyy. 4

A:

Q: For the given function 9 = x-yz and 62 -(@C) at C= 3x?yi+ yz²j- xzk, Find 5yöz бубz point (1, – 2, –…

A:

Q: Q.3. Determine the convolution of the continuous-time signals given below; y(t) = x(t) * h(t) = ?…

A:

Q: Given the function z = f(x,y) = x²y + 2y² + 4xy-2, find the following: a) Find all of its critical…

A: Here, we need to find the critical points.

Q: Let Dy be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: The linear transformation Dx:C'a,b→Ca,b maps a function fx to its derivative Dxf. Here, given that…

Q: d) The function +(xy)-r*r2y) exp G 18xy is homogencous in of degree X and

A: The given function is: f(x,y)=(x2+2y)e2xy+8xy...(1) The function f(x,y) is said to be homogeneous…

Q: Let Dx be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: Linear transformation

Q: xy ) Suppose thot fixy)=e , x(4,0)= 3uSiina, glu, vl = f(x (4,v), yluiv), find , by using Chain Rule

A: Using the chain rule,

Q: The fuel-cost functions for the three thermal plants is $/h are given by C, = 400 + 5. 5P, + 0.006P…

A: The given constraint: 50≤P1≤15050≤P2≤20050≤P3≤300 Where P1, P2, P3 are the loads of the generator…

Q: If g(x)=- A B d- ſ ^ [e' − In(2t + 1) ]dt, find g*'(x) . dx -2 2 (2x + 1)² 4 et + (2x + 1)²…

A:

Q: : Find y(0.5) for y'=-2x-y, y(0) = -1, with step length (h= 0.1) using Runge-Kutta.

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find dwdt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before…

A: (a)

Q: find the values of C1 and C2 so that the given functions will satisfy the prescribed initial…

A:

Q: Suppose that the constant rate of change of y with respect to z is 4.6. Based on the above…

A: Rate of change of any function is the first derivative of the function with respect to variable on…

Q: Find all critical values for the function f(t)=(t^4)-(12t^3)+(16t^2)

A:

Q: First write the function y = Vx2 +1 as a composition of y = f(u) and u = g(x), and then dy apply…

A: y=x2+1y=f(u), u=g(x)To find:dydx

Q: a.) If     f(x) dx   = 4x9 − 8x6 + C, find f(x). f(x) =

A: Given: ∫fxdx=4x9-8x6+c                                          ..1 for finding fx, we differentiate…

Q: --—-^[e'-In(2t+1)]dt, find g''(x) . dx -2 If g (x) = (A) (В Ce*- D 4 (2x + 1)² e* - In (2x + 1) 2…

A: We have to solve integral

Q: Let Dx be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: Solution: Consider the given linear transformation : Dxf = 2x + 3 Since D is the linear…

Q: Let Dx be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: We have to solve above question and find preimage function

Q: Given that g(2)=5 and g'(2)=3, linearize g(x) near x=2 and use this linerization to approximate…

A: Consider the linearization formula for g(x) near x = a.

Q: dz Suppose z is a function of r and y, and csc Vr2 + yz = zesin z. Solve for dz and dy

A:

Q: d Use the chain rule to calculate f(x) if f(x) In (1+ tº) dt. dx, 0. f(x) =

A: let's use chain rule and find derivative of integral.

Q: 8. DETAILS SCALCET9M 3.10.003. Find the linearization L(x) of the function at a. Rx) = Vx, a = 64…

A: given,

Q: H(x, y)  =  ln(3x2 + 9y2) (a) Find  fxx(2,3) . (b) Find  fyy(2,3) . (c) Find  fxy(2,3) .

A:

Q: 2 2t #6) A) Evaluate: t´e“dt

A:

Q: df Find dx by using chain rule if f = u =-1 , x=-1 u+1

A:

Q: 2. Suppose that z is a function of a and y, and F(x2 - y², xy - 2², yz - 2²) = 0. Calculate and…

A: Solution :

Q: Given f (x) = x³+3, let L(x) be the linearization based at 4. Find L(4)

A:

Q: dx Suppose y = x4 – 2x + 1, and both x and y are functions of t. If dt when x = -1. dt = 2, find 12…

A: Given Data The equation is y=x4-2x+1. The derivative of x with respect to t is dxdt=2. x=-1.…

Q: d²z d12 given that z = In a) Use chain rule to find dt2 x = est and y = t².

A: Derivative of the function

Q: (b). Examine the behavior of e*+iy as x → -.

A: Euler's formula states that for any real number x  Any complex number z = x + iy,  can be written…

Q: Consider the following w-xyz, x s 4t. y-s-4t, z- st (a) Find dw/ds and dw/dt by using the…

A: If F=f(x,y) and  x=g(t) and y=h(t),then     ∂F∂t=∂F∂x∂x∂t+∂F∂y∂y∂t

Q: Consider the expression: ey = 4x + y* , In which y is an implicit function of x , after derivation…

A: Given problem :- ey =4x+y4 , find y'