Calculate r' (t) and T(t), where 88.8 r' (t) = ( T(t) = ( r(t) = (3t6,2 - 3t, 2t - 9).

Q: Verify that f'(x) = 18x² – 9, where f(x) = 6x³ – 9x – 9.

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Q: Find y': 5a? – 2x?y? + 4y3 – 7 = 0. |

A: Explanation: Given that,  5x2-2x2y2+4y3-7=0

Q: Let f(t) = (t² + 4t+6) (7t² + 3). Find f' (t). f' (t) Find f'(3). f' (3) =

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Q: Vx t3 dt dx 'V2 t2-1 d limx¬

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Q: 3 y 1 8 Find the value of y.

A: Given,

Q: Question text Verify the Mean Value Theorem for the function f(x)=2x' + x? -4x-2 in [0.1]

A: Since you have posted multiple question in this question so I have solved first question as per our…

Q: For the function f (x) = 5a- 7x +4r + 3 %3D a. Find f '(x) b. Find f" (x) c. Find f" (0) and f “ (2)…

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Q: 1 I = J dx (1-x²)Z %3D 3

A: It is known that: 1-cos2x=sin2x∫sec2x=tan x+Ctansin-1x=x1-x212

Q: 8. After p practice sessions, a student could perform a task in T (p) = 36(p + 1) 3 minutes. Find…

A: After p practice sessions, a student could perform a task in T(p) = 36(p+1)3 minutes We have to find…

Q: Va –2 -dx aㅎ (V+1)

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Q: f(x)= x2/5 Where it concave up/down?

A: To find the concavity of the given function.

Q: 2. Find f'(1) if f(x) = 3x³ (√x-2).

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Q: f(x) = '(x) = - 15 √√x

A: Given query is to find indicated derivative.

Q: ((x/y)/z)+(x/(y/z))

A: In mathematics, precalculus is a set of course that includes algebra and trigonometry to prepare…

Q: Use the equation f(x)= x³ –1 to determine: f(3) = ? а. b. If f(x) = 7,then x = ? с. f"(26) = ? d.…

A: Solution:Given  f(x)=x3-1To find:(a)f(3)(b)f(x)=7  then x=?(c)f-1(26)(d)f-1(63)

Q: f(t)= 140/3 t^2 + 3000 does concavity for f(t) change . t is in days

A: Given : f(t) = 140/3 t2 + 3000

Q: 3 find f'(x). x2 7 If f(x) = 7+ -+

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Q: y²-6x²y=-9x ; y' at (1,3)

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Q: f(x) = C

A: Here we apply quotient rule of differentiation given as ddxuv =vdudx-udvdxv²

Q: Show that cosh (3x) = 4cosh³r - 3 cosh T.

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Q: let hG) = f(x) %3D where f(-3) = 7, f'(-3)= - 9, g(-3) = -2 and gʻ(-3) = 1. What is b'(-3)? %3D %3D

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Q: 9. f 6 sec¹ xdx

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Q: f(a)=9 I'(a)= 5 = -4 $()= 5 • If glx)=1F[=), find gʻ(2) -1f hlx)=f(casx), find hi(M%)

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Q: If f(t) = (t² + 6t+ 3) (5+²+3), find f'(t). Find f'(2).

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Q: Q2-Prove that

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Q: Let y = xbex (where b is a real number). Determine y'.   Let y = (3x + 6)/(6x + 12). Determine y'.

A: given y=xbex to find the derivative y' use the product rule uv'=uv'+vu' therefore,…

Q: find f'(t) for f(x)=x/8x-8

A: We will need the quotient formula to find f'(x) Assume u and v, then find u' and v'