A. Find the function f that satisfies the equation / f(1) dt : 2 cos x + 3x – 5. d B. Evaluate: dx 3 dt t - x2

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

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Q: The equation dx/dt = kx is both separable .4 and linear اخترأحد الخيارات

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Q: dA find dt dx 1 IfA%3D х? аnd 3 when x = 10, dt

A: our objective is to find the derivative at x=10.

Q: Compute the following derivative. [P(i+5j-5tk) (e'i + 5 e'j-3e -k)] dt [P(i+5j-5tk) (e'i+ 5…

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Q: Assume that all variables are the function of t. If 5x2 - 4y3+3y=D7 and dy/dt 2 when x-11 and y=3.…

A: Take the derivative of the given equation with respect to t and substitute all the values than solve…

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 4 cos x – sin xy; y = 7t || Enter the…

A: We have to find

Q: dw Use an appropriate form of the chain rule to find dt w = 4 cos xy – sin xz; 1 x = ; y = t, z = t8…

A: A detailed solution is given below

Q: dz dS 2 If S = z3 and -2 when z = 3, find dt dt

A: Derivative

Q: (a) Evaluate the following derivatives: d ) cos(V5r" - 2)át. s(V5r² – 2)dt . (i) dx J2 d cos V5t – 2…

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Q: use the Chain Rule to calculate f (r(1)). dt f(x, y) = x² – 3xy, r(t)= (cos 1, sin t), t=0

A: Given: fx,y=x2-3xyrt=cost,sint

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

A: Given:         8y3+x2=1dxdt=2x=3y=-1 Differentiate 8y3+x2=1 with respect to t,…

Q: t F(x) cos(3t – 1) dt sin z %3D

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Q: d Find the value of f(x) if f(x) : cos (t) dt. dx. COS f(x) =

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Q: Q3) Find dy/dt of the function y = cos (5sin (t/3))

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Q: Q3.a) Find if y + SE 1 dt = xy (secx dx sint+1

A: My dear, as per our guidelines we can help you in solving only first problem. Rest of them , you…

Q: dw Use an appropriate form of the chain rule to find dt 1 y = t, z = to w = 3 cos xy – sin xz3; t'…

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Q: Use the fundamental theorem of calculus and the chain rule to find (A(x)) where dx e2x A(x) = In(t?)…

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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: b) f(x) = In(1 – 3x) %3D c) f(x) = cos(t³) dt

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Q: If F (x) = (t2) dt , then F' (4) = cos 0,

A: DUIS rule is used

Q: d use the Chain Rule to calculate f(r(t)). dt f(x, y) = x² – 3xy, r(t)= (cos t, sin t), 1 = }

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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: dx 1-t+ x-tx dt

A: Given, dxdt=1-t+x-tx The equation is separable. Write it in differential form and integrate both…

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 6 cos x – sin xy; x = y = 6t t' Enter…

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Q: dz Use an appropriate form of the chain rule to find dt z = 7 cos x – sin xy; x = ;, 1 y = 9t Enter…

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Q: dF find F (x) = J- dx but -x cos(tx) dt t

A: A

Q: If F(x)= J. x) = [", "+!dt then F'(x) dt , then F'(x)= /3 sint

A: If Fx=∫π3xt2+1sintdt, then evaluate the value of F'x.

Q: Let z = x?y + 3xy+ where x = sin 2t and y dz find = cos t. Use the chain rule to when t = 0. dt

A: See solution below. Using definition of chain rule.

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 8 cos a – sin xy; x = - y = 4t t'…

A: This question is based on Derivative of Function.

Q: dz Use an appropriate form of the chain rule to find dt z = 7 cos x – sin xy; 1 y = 7t Enter the…

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Q: dw Use an appropriate form of the chain rule to find dt 1 w = 8 cos xy – sin cz; x = y=t, z = t7 t'…

A: Here we have to find dw/dt by chain rule.

Q: Find j cos(VF +1 +1)dt dx

A: Using the leibnitz integration problem.. Explanation of the solution is given below..

Q: Let T = x²y - xys + 6x, where x = r cos 0 and y = r sin 6. Use the chain rule to find dT/00.

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Q: The

A: This is Linear Differential equation in x. We use method of separation of variables.

Q: E. Find , and in terms of dx dt' dt 1. x = t°- 1 2. x = 4t + 3 y = 3t – 2 y = 4 - t

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Q: Solve the initial-value problem for a as a function of t . dx (t2 – 11t + 24) = 1, (t > 8, x(9) = 0)…

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Q: cos(x) If f(x) = ["(@) "g(x) V1 + t3 dt, where g(x) = S [1 + sin(t²)]dt, find f'(;). 1 %3D

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 6 cos x – sin xy; Y = 8t %3D t' Enter…

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

A: Given gx=12∫x4x2costdt  -x2

Q: g(x) f(x) - sin(2²) dt, find f(x). = J

A: To Find: f'(x)

Q: Evaluate the following derivatives: a) d V1 +* + 1° a dt dx 7, b) 10 d dt dz sin(z) 14 +1 c) :/ Vi+?…

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Q: assume x and y are functions of t.  Evaluate dy/dt for the following: y3=2x4+6; dx/dt=2, x=1, y=2

A: The given function is  y3 = 2x4 + 6    ...... (1) dx/dt = 2, x = 1,   y = 2

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

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Q: Assume that all variables are the functions of t. If 3y2-2x2+4y=2x and dy/dt =4 when x-9 and y=12.…

A: Given,  3y2-2x2+4y = 2x   and dydt= 4  when x = 9  and y = 12  Then, we have to find the value dxdt…

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 5 cos x – sin xy; y = 4t t' X = Enter…

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Q: Assume x and y are functions of t. Evaluate DY/DT for 4xy-4x + 6y^3 = -258, with the conditions…

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Q: Identify the Bernoulli's equation of first order ODE. а. dy +10xy = y sin x dx ,3 b. dy +10x²y = sin…

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

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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'

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Q: f(æ) = / t2 – 9 dt 1+ cos? (t) At what value of x does the local max of f(x) occur?

A: Given: For the local maximum value of f(x), we must have f'(x) = 0. Here,…