dz az Use the chain rule to find and as sin(8) r = st, 6 = s + t3 = az %3D as az %3D

Q: T/2 cos(9t) cos(18t) dt

A:

Q: dw Use the Chain Rule to find where w= cos 12x sin 4y, x=5, and y =t". dt dw dt (Type an expression…

A:

Q: If y = tan(4x + 1), determine using chain rule. dy dx

A:

Q: use two and three points of Gaussian-Quadrature method to Find 1 = e" e(1+sinx) dx

A:

Q: sinh(3z+1) z2 - 5z+6 Evaluate dz, where C : |z– 2i|= 1, counterclockwise.

A: We have to evaluate ∮Csinh3z+1z2−5z+6dz, where C:z−2i=1, counterclockwise. Cauchy Goursat theorem:-…

Q: is If У%3D2х arccos x - 2/1-х? then dx

A: We differentiate both sides with respect to x and then solve it.

Q: 03: Use chain rule to find dy/dx for the following 1. y = -sec u, u = x² + 7x

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

Q: tan 0 d 30. dO sec² y dy

A:

Q: use the chain rule to find: 28) dv 2- COSxy + y cos x

A: Solution:Given   z= cos xy+ y cos xx=u2+v and y=u-v2To find :dzdvFormula:ddx(cos x)=-sin…

Q: Q5) Use the Chain Rule to express dy /dx in terms of x and y: y = csc t and x = sec-1t

A: To find: The value of dydx in terms of x and y. Given information: y=csct,x=sec-1t

Q: Find 17. d Ssin (4x) cos(4x) dx

A: Use substitution to solve

Q: (sin 2x)y' = y cos 2x

A: Consider the given Differential equation, sin2xdydx=ycos2x divide both side of the differential…

Q: 1. Lif f(x,y,2)=2exp(-5xyz)cos(15z) Find ôxôz

A:

Q: Solve if the set of functions (1, x, sin x, e^x, cos x) is linearly independent or dependent…

A:

Q: dw Use the Chain Rule to find , where w = sin 8x cos 2y, x= and y =t. dt dw dx (Type an expression…

A: Chain rule

Q: (1+cos(4t) dt 2

A: Let's find integration of given function.

Q: y = 46 tan B3 – 2 = 4¢ tan az – 2 %3D and y = 46 tan B2 +2 = 46 tan æ3 + 2 %3D and hence all the gas…

A:

Q: RFind dy/dx in terms of x and y if cos²(8y) + sin²(8y) = y+4. |

A: Given query is to find the derivative of the given expression. Pp

Q: 2z2 cos 5z dz EVALUATE.

A:

Q: T c •sinx, S* San* (1 + cosx)dydx 0, 0.

A: Given: The integration ∫0π∫0sinx1+cosxdydx To determine: The value of given integral.

Q: Find y' cos(xy) - y^4 = 5 - 3x

A:

Q: If Z = Jxy +y, x= cos 0 , y= sin 0 when 0 dz By using chain rule find de

A: Chain rule for one independent variable- Suppose that x = g(t) and y = h(t) are differentiable…

Q: find δƒ/δx and δƒ/δy. ƒ(x, y) = cos2 (3x - y2)

A: Consider the provided provided function, fx,y=cos23x-y2 Find the partial derivatives of the function…

Q: use the chain rule to find dy/dx for the followingy=sin^2 (3x-2)

A: Firstly, we introduce two new functions u(v) and v(x) as shown on board.

Q: use the chain rule to find dy/dx for the followingy=cos(pi/2 -3x)

A: Calculation:

Q: Find ??/?? using the appropriate Chain Rule w = ln y/x; x cos t; y = sin t

A: Use chain rule.

Q: dz and du dz Use an appropriate form of the chain rule to find dv ; x = 16 cos u, y = 3 sin v Enter…

A:

Q: 94. Find dy/dx if y - 2 by using the Chain Rule with y as a com- position of a. y- u' and - V b. y -…

A: a) Given y=x32 The chain rule state that dydx=dydu·dudx

Q: fCx) at c0,2) で +x + co.2) 2. メ 2/3

A: Given curve is fx=23x2+x+2. To find the equation of tangent line and normal line of the curve at…

Q: 1 and y' CO)

A:

Q: Find dy/dx by using Leibniz’s notation for the chain rule: dy/dx = (dy/du) (du/dx) y = (tan x + sin…

A: The given function is y=tanx+sinx-3 We have to find dydx by using Leibniz’s notation for the chain…

Q: dz when du Use the Chain Rule to find = e' cos 0 and r = 3uv, 0 = Vu? + v². sin A

A:

Q: A ) Find ſ cos 5t dt B) If y = x² + , x = 2t -5 then find dt

A: A)-     I=∫Cos5t dtlet 5t=uderivating both sides5 dt = duSo,I=15∫Cos u du = 15 Sin u +C…

Q: Show that y1(t) = cos(3t) and y2(t) = sin(3t) are linearly independent for all t

A:

Q: Solve by Chain Rule g(t) = sin (e1-t + 3 sin(6t))

A: Solution is written in below steps.

Q: az Use an appropriate form of the chain rule to find dt 1 z = 2 cos x sin xy; y = 5t t Enter the…

A: z=2 cos x-sin xy ; x=1t; y=5t   see z is a function of x and y ,where x and y are functions of t so…

Q: 2x Cos 23 find diy %3D

A:

Q: use the chain rule to find dy/dx for the followingy=cos(sinx)

A: To find the derivative of the given function y = cos(sin(x)).

Q: d (cos² 2x)=-2sin 4.x dx 12 Show that %3D

A:

Q: 3. Given that 2 = 6²¹ sin (u + ), e2v Use chain rule to find az/0x when x = 0, y = 0. u=e¹ - sin (y…

A:

Q: az and az Use a chain rule to find the values of dr Ir=12, 0=x/6 Ir=12, 0=n/6 if z = xye"/v, x = r…

A: Solution:

Q: e sec(3x+2) sin(3x+2) dx Evaluate cos² (3x+2) -3e sec(3x+2) + . O 1 ,sec(3x+2) + C 3 1 ,sec(3x+2) 3…

A:

Q: The function z =x^2√y is defined on the astroid x = cos^3θ, y = sin3θ where 0 ≤ θ < 2π. Use the…

A:

Q: 1. If y = cos(2t + 5) find using chain rule dt

A: Giveny=cos(2t+5)

Q: .2 Suppose that w = x² + y² – z2 And x = psin(4)cos(0), y = psin(4)sin(0), z = pcos(4) Use…

A: The Solution is given in next steps

Q: i. f(x) = Cos?(3Vx) (using chain rule)

A:

Q: eš(secy

A: To find derivative of eysec2y

Q: Find LT of (i) e-*(2 cos 5t – 3 sin 5t) (ii) e²ª cos² t (iii) e“ sin 2t cos t ,4t

A:

Q: 3: Solve ODE Cist Order a. dY

A:

Q: 3. y" + 2y' + 5y = t cos(5t) - 6,y(0) = 1, y'(0) = -2

A: