Let u(æ) = sin(x) and v() = a = 18 and f(x) (*)a u (2) -| v (2) = u'v – uv f'

Q: Let F(z) = f(cos(x)) · sin (금) and G(x) = f(sin(x)) · cos : (주) and suppose that f(0) = 5, f(1) =…

A: We have to find

Q: find (a) r'(1), (b) r"(1), and (c) r'(f) • r"(f).

A: The derivative of a position vector gives the rate of change of position of the body or the velocity…

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: 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: Let f(æ) = In a*(x + 5)*(2² + 4)*| f'(x) =

A: We will use properties of logarithm. lnan = n lna  ln(a.b) = lna + lnb

Q: 3 Find f'(x)given f(x) = x/x – 4x – 7x %3D

A:

Q: Suppose y is a function of x. Find y' given csc-1y + xy = sec 1 y.

A: Given, csc-1y+xy=sec-1y

Q: Let f(x) = 1 Find f' and f" (the first and second derivatives).

A: f(x)=13-x

Q: Use the graph of f and g. Let p(x) = f(x)g(x) and g(x) 2 (a) Find p'(4). p'(4) = = (b) Find q'(1).…

A:

Q: Use the rule for square roots: f'(x) 2/ F(x) V F(x) to find the following derivatives (quickly d V…

A:

Q: Let h(x) =tan(3x + 5). Then h' (4) is 3 sec² (17) 2 and h''(4) is

A:

Q: If f(x) = cos-(r"), then f'(x) = (A) (B) (C) (D) (E) -32? sin-(æ³) (A) O (B) o (c) O (D) (E)

A: We have to find derivative

Q: Let g(x) = 2 f(u) + 3 where . u = x² + 2x. What is the derivative of g with respect to x? ○ 2. f'…

A: Given that, the function is gx=2·fu+3 and u=x2+2x. By the chain rule formula ddtFut=F'ut·u't.

Q: Let h(x) = tan (2x + 6). Then h'(2) is and h'(2) is

A: topic- functions and derivatives

Q: Let f(u) = u* and g(x) =u = 2x* + 6. Find (fo g)'(- 1). (fo g)'(-1)= (Туре an exact answer.)

A: Given:- Let f(u) = u4 and g(x) = u = 2x4 + 6   To Find (fog)'(-1).

Q: Let h(x) tan(5x + 7). Then %3D h'(4) is and h''(4) is

A: As in question it is not mentioned wheather we have to considered degree or in radian inside…

Q: Let f(z) = cos and g(z) = tan-(10z) Then if h(z) S(z) find: 9(z) h'(1) = N(즉) = |

A: The given functions are  f(x) = cos-1x/5 , g(x) = tan-110x   If, h(x) = f(x)/g(x)  Find h'(x) and…

Q: 2. If g(x) = (ƒ 03ƒ •4f)(x) = ƒ (3ƒ (4ƒ(x)). Determine gʻ(3), given f(3) = 1, ƒ(4)=1, ƒ'(3) = 2 and…

A:

Q: Let f(x) = sin(x5). f'(x) = f'(2) = 0

A: NOTE: Refresh your page if you can't see any equations. . take derivative

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: Let F(x) = sin(x) ex a) Find f'(x), F"(x), f (³) (x), F"" (x) b) Find f (2) (x), the 2n-th…

A: Here, we have to find the derivatives of f(x)=sin(x)exWe shall be using the product rule of…

Q: (a) Let f(z) = sin*(z). Find f' (x), T(2) = (b) Let f(x) = J (x) = sin(z³). Find f'(x). %3D

A:

Q: y = 3x sin-(x²) + In(1 + 2x). Find y' using derivative rules

A: The given function is as -y = 3xsin-1(x2) + ln(1+2x)Differentiating on both sides with respect to…

Q: Find f. f'(t) = sec(t)(sec(t) + tan(t)), = -1 f(t) =

A: Given that: f'(t)=sect(sect+tant),    -π2<t<π2, fπ4=-1

Q: Find f. f(x) = f"(x) = 5ex - 7 sin(x), f(0) = 3, ( 77 ) = 0 EN 2

A: Given :f''x=5ex-7sinx

Q: Let f(æ) = (x – 9)* – 5, determine f-(x). f\(x) =|

A: We need to find inverse function.

Q: Let f(x) = sin(z))". Find (1). (1).

A:

Q: (a) Let f(r) = sin (1) Find f'(x). f'(x) = (b) Let f(r) = sin (ar). Find f"(x) f'(x)=

A:

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of » sin ( z ) h(2) = | .…

A: simply put at the place of sinx and multiply it by differentiation of sinx

Q: Let f(u) = Vu and g(x)-u-5+ 12x Find (fo g)'(1). (1),(6 • ) = an exact answer.) (Type

A:

Q: Letr' (t) = (3 + 4t, cos(t), 6e³t) and 7(0) = (7, 2, 5). Determine r* (t). r(t) = ([ (..)

A:

Q: Find f'(2), where f(t) = u(t) - v(t), u(2) = (1, 2, -1), u'(2) = (8, 1, 6), and v(t) = (t, t², t³).…

A:

Q: Find y as a function of a if = y"-7y" +12y = 6e², y(0) = 24, y' (0) = 16, y" (0) = 27. y(x)=

A: