(a) If w = e"yz, where x = and compute dw/dt when t = 0. (b) If f(x, y, z) function of s and t and compute df/ðs when (s, t) = (0,0). = 3t, y = 1 – t, and z = 2t + 5, find dw/dt as a function of t = x cos(yz), where x = s' 2, y = t2, and z = s – 2t, find ðf/ðs as a

Q: find dy/dx

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Q: Q3) for f(v) = sec2(3v – 1) and g(v) = tan?(3v – 1) show that %3D %3! f'(v) = g'(v).

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Q: Find the derivatives of y with respect to x: a) y = xe* - e* b)' y = e(4x+) e(tx+) X. c) y = e*(sin…

A: Since you have posted multipart question and we can answer three subparts. So, answered first three…

Q: .3 Find f'(t) if f(t) = 8t° + 5t + 4. f'(t) =

A: Consider the function  f(t)=8t3+5t+4

Q: Find the derivatives of y with respect to x: a) y = xe* – ex b)' y = e(+x+) c) y = e*(sin x + cos x)…

A: Differentiate the function with respect to x.

Q: For the linear operator L = D^2 −4D + 8, determine L(y) for y = e^(2t), y = e^(2t)sin(2t), and y =…

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Q: 2. Find the gradient of the function f(x, y) = ln(x² + y²) at the point(1, 1).

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

Q: Let f(x, y, z) = x“y + z* and x = s³, y = st°, and z = s°t. (a) Calculate the primary derivatives ,…

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Q: Find r'(t). 13 r(t) = 3 cos (t)i + 5 sin (t)j + k %3D r'(t) %3D

A: Given:

Q: a) Suppose that f(4)=3 and f'(4)=-5. Find g'(4) where g(x)=Vx f(x) b) Let y=cosx-sin.x , show that…

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Q: Ex: Find the F.T. of the rectangular pulse (gate function). f(t) = A rect ( =) = ATT (t/), I is the…

A: Hint: We need to find the Fourier transformation of f(t)=A rect(tτ)

Q: Find f. f "(t) = 5e + 8 sin t, f(0) = 0, f(x) = 0 f(t) :

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Q: Consider y=(x2+1)2x a) find dy/dx b)Evaluate y'(1)

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Q: Write the system x'= e"x – 4ty+9 sin(t), y' = 7 tan(t)y + 9x – 4 cos(t) in the form = P(t) + F(t).…

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Q: Suppose z = f(x, y), where f is differentiable, x = g(t), and y = h(t). If g(5) = 8, g'(5) = 9, h(5)…

A: Given that z=fx,y, where f is differentiable. Here, x=gt and y=ht. Also, let, g5=8, g'5=9, h5=-7,…

Q: For f(x1, x2) = x2 cos x1 find f'(x1, x2), f'(2,7) and df[(2,7); h]. For f(x, y, z) = (x – 2z)e"…

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

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Q: W = x =t' +7, y=cos(2t), z=4t COS

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Q: Suppose r' (t) = (cos(t), et, 2t) and r(0) = (1, 0, 3). Find r(t).

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Q: Let F = (3t + 2) i + sin(2t) j+ 3ť²k Find F'(t), F"(t) and F"(t) 1) F'(t) = (2) F" (t) 3) F" (t) =

A: Solve for the equation for the derivative

Q: dw Use the case 1 chain rule to determine the derivative where dt ม w(x, y, z) = xez and x(t) =…

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Q: Suppose f(x) = [ 6t² /1+t° dt .

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Q: 2.15 Some sets of probability distributions. Let r be a real-valued random variable with prob(r =…

A: The solutions of 2.15 are given below

Q: Find f. f"(t) = 5et + 4 sin t, f(0) = 0, f(1T) = 0 f(t)

A: topic- differential equation