Find f'(3), where f(t) = u(t) · v(t), u(3) = (1, 2, −1), u'(3) = (8, 1, 6), and v(t) = (t, t², t³). . f'(3) =

Q: Calculate r' (t) and T(t), where r(t) = (6 +5t,9 – 61, 2t). r' (t) = ( ). T(t) = ( ).

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Q: = f(x) g(x) If f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = y 6…

A: The given graph of the functions is shown as,Let,Note:  As mentioned in the instruction, we are…

Q: Let F(x) = f(f(x)) and G(x) = (F(x))² and suppose that Find F'(8) and G'(8). = F'(8) = G'(8) = ƒ(8)…

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Q: Find f '(2), where f (t) = ü(t) · i(t), ü(2) = (1,2,–1), ū'(2) = (3,0,4), and v(t) = (t, t?,t3).

A: To find out the f'(2)

Q: Find f'(3), where f(t) = u(t) · v(t), u(3) = (1, 2, -1), u'(3) = (5, 1, 4), and v(t) = (t, t², t³).…

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Q: Let r(x) = f(g(h(x))),where h(1) = 2, g(2) = 3, h'(1) = 4, g'(2) = 5, and f'(3) = 6. Find the value…

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Q: If r(t) = , find r '(t), T(1), r ''(t), and r '(t) ✕ r ''(t).

A: Given  r(t) = <4t, 6t2, 2t3>

Q: Your used Chevy’s gas mileage (in miles per gallon) is given as a function M(s) of speed s in miles…

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Q: et f(r, y) (-(4r + y)) Then %3D ardy

A: The given differential equation is: f(x,y)=-(4x+y)7

Q: Find r'(t), r"(t), r(t)•r"(t), and r'(t) × r'"(t). r(t)-흑러 - 26 + (a) r'(t) (b) r"(t) (c) r'(t) ·…

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Q: Let F(3) = 1, F'(3) = 5, H(3) = 2, H' (3) = 2. A. If G(2) = F(z) · H(2), then G' (3) B. If G(w) =…

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Q: Let h(x) = f(g(x)). If: f(3) = 0, f'(42) = –5, f'(3) = 4, g(3) = 42, & gʻ (3) = 0, then h'(3) =

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Q: Let r(x) = f(g(h(x))), r'(1) = where h(1) 2, g(2) = 3, h'(1) = 4, g'(2) = 5, and f '(3) = 6. Find…

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Q: Find f. f ''(t) = 12/sqrt(t)                          ,    f(4) = 38,    f '(4) = 18   Recall that…

A: Given Integrating both sides, we get But f'(4)=18

Q: nd r'(t), r"(t), and r'(t) · r"(t). r(t) = 4 cos(t)i + 3 sin(t)j a) r'(t) b) r"(t)

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Q: Let F(4) = 2, F'(4) = 4, H(4) = 2, H'(4) = 3. %3D A. If G(2) = F(z) · H(2), then G'(4) = %3D B. If…

A: Given : F4 = 2, F'4 = 4, H4 = 2, H'4=3

Q: Differentiate h(t) = (rª – 4)³(1³ + 4)ª. h'(t) =

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Q: If f (x) = 3x²-2 4x+1 then f'(-1) =

A: Given

Q: Find f '(a). f(t) =  3t + 9 t + 8

A: Explanation of the solution is given below...

Q: If ř(t) = (t,t², t³), find 7 '(t),T(1),7 "(t),and i '(t) xi "(t).

A: Unit Normal Vector , T(t) = r'(t)r'(t).

Q: Let r(x) = f(g(h(x))), where h(1) = 2, g(2) = 3, h'(1) = 5, g'(2) = 3, and f(3) = 6. Find r'(1).…

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Q: Find f such that f'(x) = f(x)= f(16) = 21.

A: Topic:- application of integration

Q: Find g'(4) given that f(4) = -1 , f'(4) = -2 , and g(x) = Vãƒ(x).

A: Use the product rule to find the derivative of the function:

Q: Let g(x) = xe2r +1. Find g'(x). Don't simplify your answer. (а) 3. Let h(t) sec(t2). Find h"(t).…

A: (a)Given:

Q: If r' (t) = (0, 0, t2) and v(0) = (1, 0, 0,), find v(t).

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Q: Let h(t) Then h' (t) is h' (3) is 2+3.2 = h'' (t) is and h'' (3) is 6t-3.2

A: Let ht=2t3.2-6t-3.2.Then find  h't,h'3,h''t and h''3.

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = 5t²i – 3tj + _t3k (a) r(t) 5ti - 3j +…

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Q: If f(r) = t dt then f'(x)

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