Differentiate the function. r(t) = (3²- + 8)i + r'(t) = (6t)i + ( 132 r'(t) = i + (6t)j r'(t) = (6t)i- 15 r'(t) = (6)i + 15 25

Q: ƒ' (4) = If f(x) = 3√√√x(x³ − 2√x + 2), find f'(4).

A: Given that

Q: If ƒ(t) = (t² + 6t + 7) (7t² + 2), find f'(t). Find f'(2).

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Q: Give the value(s) of x at whichf has either a local minimum or a local maximum. Give the interval(s)…

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Q: (S dx (f(+ 2t)° dt (2+3x)

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Q: Find f. f"(x) = −4+ 8x - 12x², f(0) = 4, f'(0) = 12 (Prob. 1,

A: Consider the derivative function and initial conditions, f''x=-4+8x-12x2,f0=4,f'0=12 The objective…

Q: y' = sqrt(x + y + 1)

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Q: Using the figure below, where f' (3) = 2.1.f' (6) = 3.0,f' (9) = 3.7,f' (12) = 4.2, find (f-1)'(12).…

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Q: Find f. f"(x) = 6 – 6x – 60x³, f(0) = 2, f'(0) = 3 %D f(x) = %3D

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Q: Differentiate the function. y = ex +4+3 y' = et+4+3 X

A: The Sum/Difference Rule:The Power Rule:The Chain Rule:And use the common deriavtive:

Q: Find f'(w) for the function. 8w7 - 9w5 f(w) = 7w5 f'(w) = %3D

A: differentiate f(w) with respect to w

Q: f"(x) = 6x – 2 | and f' (-2) = 3 and f(-2) = 6. Find f' (x) = and find f(4) =

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Q: Find the first and second derivates of the functions. h(t) = t^4 - 7t^3 + 5t^2 - 8t - 14…

A: Find the first and second derivative of the function

Q: IF F"(X)=12X^2+24X-6 ,  F'(1)=10,   F(2)=20 , determine the function f.

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Q: Differentiate the function. y = V7 + 4e3x y' = %3D

A: The function is  y=7+4e3x

Q: Find f '(a) f(t)6t12 t 7

A: The given function is

Q: y' = x2y2/x2+y2 ; is this function seperable or non-seperable

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Q: Find f. f ''(t) = 9/ squareroot t,    f(4) = 31,    f '(4) = 12

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Q: f(x,y)=x^4+y^4-4xy Find all the endpoints of the function.

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Q: Find f. f(x): = f"(x) = -2 + 30x - 12x², f(0) = 5, f'(0) = 12

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Q: If f(x) = 3/7(2 – 7a + 5), find f'(x). - Find f'(3).

A: Given:- f(x) = 3√x(x3-7√x+5)  To find:- f'(x) and f'(3)

Q: For the function f(x) = (3x + 5)4, find f''(x), f''(0), f''(2), and f''(-3).

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Q: The functions f and g are differentiable and h(x) = f(g(x)). Use the information below to find…

A: We know that If h(x)=f(g(x)) then h'(x)=f'(g(x))g'(x)

Q: Find f' (x) for ƒ (x) = 8x° – 3e".

A: Given : fx = 8xe - 3ex

Q: Find f. f ''(t) = 9/square root of t,    f(4) = 26,    f '(4) = 13

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Q: Find f. f"(x) = -2 + 30x – 12x2, f(0) = 8, f'(0) = 16

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Q: Find the quadratic function such that f(4) = - 26, f '(4) = -19 and f ''(4) = -6.

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Q: 24. (EXERCISE) Consider the function f(x)=3x* – 20x' + 42x² – 36x

A: The given function,   f(x)=3x4-20x3+42x2-36x