Differentiate the following function. r(t) = (3t e -,3t In t,t cos t) r'(t) = (OOD

Q: Complete the table by "breaking down"the function into the inner"and "outer" Function dy du dy u du…

A:

Q: Q2/ find dz ond dZ as function ne U and v if of Z=tan (중), X=u Cos V , 9-u sinV

A:

Q: dw Find the value of- dt at the point (1, In 2 ,0) on the curve x = cos t ,y= sin t, 0 <t< 2n where…

A:

Q: Find for the following function. dx 6 cos x y = 6-5 cos x dx

A: To find the derivative of y.

Q: a. Evaluate the following derivative d tổ tan(t) dt. sin(x) dx

A: We will use the Newton Leibniz formula to evaluate the differentiation

Q: al derivatives of t 'sin(z+y)

A: According to our terms and condition i have solved first question for next question repost

Q: dy Find the differentiation ) of the followings using the chain rule: dr2 y = (3 – sin'(r3 + 1))2.

A: The given equation is  y=3-sin-1x3+12 We have to find the second derivative using chain rule. Also…

Q: Apply the Fundamental Theorem of Calculus to get the following derivative. d. In( t?+1) dt dx 1

A: Given, fx=ddx∫1x3lnt2+1dt To Find: f(x) by applying fundamental theorem of calculus.

Q: Apply the Fundamental Theorem of Calculus to get the following derivative. d In (t² + 1) dt dx 1

A:

Q: Let x = x(t), y = y(t) and z = z(t). Differentiate the following function with respect to t. 2°…

A:

Q: Consider the following. w = cos(x − y),    x = t2,    y = 21 (a) Find dw/dt by using the…

A:

Q: Obtain the derivative of any of the following functions: A) f(x) = 3cotg²3x B) f(x) = 6cos7(3x2 – 1)…

A: Answer

Q: Consider the following function and express the relationship between a small change in x and the…

A:

Q: dy For the function dt d y is 3 cos t, the third %3D order derivative dt3 O 3 cos t

A: Given: dydt=3cost To find the third order derivative d3ydt3. Solution: We have, dydt=3cost…

Q: (c) Differentiate the following functions with respect to x. (i) х3 + 5y4 — 2 — 1. (ii) y = -…

A: Differentiate the given functions with respect to x.

Q: Q1J Use the Chain rule to find the derivative of w=xy + In z with re spect to v if x v/u, y u+v, z…

A: The chain rule is used to calculate the derivatives of the function. The chain rule for a function…

Q: Find the derivative of y with respect to t at t=2 if a) у %3D х + sinх - cos(1 + x+x?) аnd x = (t/t…

A:

Q: Find the derivative of the following function. y = In (x° +6)" dy %3D dx (Type an exact answer,…

A: Given: y=ln(x3+6)π To find the dydx=?

Q: of dx- = 0, then dy |=0. Prove that is a function f is harmonic

A:

Q: dF Q. IF the value of (t) change from x to x. Find the r(x.t) = (t-x) cos( F(x) = S(x,t) dt for…

A:

Q: Find the differential of the function. z = e ** cos(8nt)

A:

Q: Compute the derivative of the given function. g(t) = 2t*e' – 4 sin t cos t g'(1) =

A: on doing differentiation with respect to t we get

Q: Calculate the error of approximation with EA for the following functions TC f(x = 4 cos 5x when x =…

A: We know: lim∆x→0∆y∆x = dydx…

Q: Assume x and y are functions of t. Evaluate dy,dt for each of the following.:…

A: We have the given function in x and y as 2xy-5x+3y3=-51 On differentiating both of the side with…

Q: For the functions w = 8x + 3y, x= cos t, and y = sin t, express dw as a function of t, both by using…

A: The given function is w=8x2+3y2, x=cost and y=sint. We have to express dwdt as a function of t.…

Q: 4x - 6xy? + 3y² = 228; dx = 3, x = -3, y = 4 %3D

A: Given  4x3-6xy2+3y2=228 ; dxdt= 3   at     x=-3    , y=4

Q: If f (x)= [a(«) =os* '(5) [1+ sin(t?)] dt find f 1 dt, where g(x) V1+t3 COS X

A: We need to find value of derivative.

Q: dy for the following implicit function at p(1,1) Find dx Vxy +1 = y is O 1 O 1/2 O -1/2

A: A detailed solution is given below.

Q: Obtain dy from the following function y= e v*

A:

Q: H.W: Use the chain rule to find the derivative === with x = cos² t, y = sin² t, z = - at t = 3 dw xy…

A: Solution :

Q: 1) f(t) =t cos(@t) 2) f(t)=tsin(@t) 3) f(t) =t cosh(at)

A:

Q: d rx Cos t dt dx J-x Vt2+1

A: Definition used -                 The first fundamental theorem of calculus -…

Q: Differentiate the following implicit function with respect to x : b. y = -In (Ryx²) + sin(y)e³3Rxy +…

A: To differentiate the given implicit function with respect to x.

Q: Consider the following. w = cos(x - y), x = t2, y = 1 (a) Find dw/dt by using the appropriate Chain…

A:

Q: Evaluate: L{t f -t e2t Cos t dt}.

A: Evaluate: Lt∫0te2t costtdt First of all we find    L(cost)=ss2+1L(e2tcost) =…

Q: dy dy For the function dt 7 cos t, the third order derivative dt3 is %3D

A: derivative with respect to t first oder derivatinve dydt is ddt(y). (which is given in the…

Q: Find the differential of the function. Z = e cos(2nt) dz = dx + dt

A: Given,

Q: Evaluate dt dW at t=0 for the function W = e' – In x , x = t², y= In t

A:

Q: 51. grad f = (2x + 3e")7 +3xe'j

A:

Q: 13. Find the derivative of the function T(z) = dz +b cz +d numbers such that ad – bc + 0. When is…

A: Hello. Since your question has multiple parts, we will solve first question that means question (13)…

Q: Let f(x,y) = 8x + 10y with x(t) = cos t, and y(t) = sin t. Find the derivative of w = f(x,y) with…

A: Here we have to find the derivative of w with respect to t.

Q: Consider the function g(x) = 5 S cos t dt – x?. Then g' (x) is

A: Given gx=12∫x4x2costdt  -x2

Q: Consider the following. w = y? - x, x= cos(t), y = sin(t) dw by using the appropriate Chain Rule. dt…

A: given: w=y2-x, x=cos(t) and y=sin(t) (a) we have to find the value of dwdt by using the appropriate…

Q: Find the differential of the function. Z = e-8x cos(5xt) dz z = dx + dt %3D

A:

Q: Find the directional derivative of Du f(2,1) in the direction of: d = 7i + 2j To f(x, y) = In(Ges…

A: As per our guidelines we are supposed to answer only one question. Please repost another question as…

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. sin t (In t+5) 3 y e 3esint cos…

A:

Q: dw Use an appropriate form of the chain rule to find dt 1 w = 8 cos xy – sin xz; x = , y=t, z= t'

A:

Q: Find the general sebution of the oDE dy Sin(x+y)+ Cos (X+y) %3D dx

A: