4. f(x) if f(x) - In(sin?x cos?x) a. 4 tan 2x b. 2 tan 2x c. 4 cot 2x d. -4 cot 2x

Q: (a) Is Rolle's Theorem applies for the function ƒ(x) = cos(sin¬'x) on the closed interval [-1, 1]?…

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

Q: 9 If f(0) = cos 0, ·cos 02· cos 03 ... cos 0n .... .·. f' (0) f (e) Show, {tan 01 + tan 02 + tan 03…

A: Given that we have to prove where

Q: If f(x)= cos (x)+3x , what is f'(x) ? COS O f'(x)=-sin (x) +3

A: First option is correct. Explanation is given below....

Q: If S (x) = - sin(x), then f (11) (x) is equal to – sin(x) B B -cos(x) CosX sin (x) D O cos(x) A,

A:

Q: Determine the exact x– value(s) of the intersection points of the functions f (x) = 4 sin² +7 sin 4…

A:

Q: snip

A: We have been given the three functions such as  f(x)=sinx  -π2≤x≤π2g(x)=cos x  0≤x≤πh(x)=tanx…

Q: Use a CAS to plot the implicitly defined level surfaces in Exercises 73–76.

A:

Q: If f (x) = – sin(x), then f (10) (x) is equal to A - sin(x) В - cos(x) C sin(x) D cos(x)

A:

Q: Let  f(x) = cx + ln(cos(x)).  For what value of c is f'(pi/4)=4

A: sol:-    Given f(x) = (x+ln(cosx)  differentiating ω. r.t   x, we get    f1(x) = c+1cosx(-sin x)…

Q: If f cos xdx = A +B sin x + Csin²x+ Dsin³x+ Esin*x+ Fsin5x, what is , 2 ) and ( - 2,5). the value of…

A: Given: ∫cos5xdx=A+Bsinx+Csin2x+Dsin3x+Esin4x+Fsin5x.

Q: If f(x) = = cos x – 4 tan x, then find: f'(x) = f'(4) =

A:

Q: Prove that sin x can be approximated by x − (x^3/6) within 0.01 on the interval [-1,1].

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Q: Find the function that satisfies the given 4. f'(x) = 2 + cos x and f COS X = 1

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Q: For the function f(x) = sin x , with the aid of elementary formula sin2A = 1/2 (1 − cos 2A), show…

A: Given that fx=sinxfx+y=sinx+yfx+y=sinx cosy+cosx siny by addition formulaNow ,       fx+y-fx…

Q: 9. e' cos (x) =1+ sin (xy) 10. tan (x – y) = 1+ x2

A: Given the equations 1)ey cos(x)=1+sin(xy)2) tan(x-y)=y1+x2We need to find implicit differentiation…

Q: If f(x) = COS x 3 tan x, then find: | f'(x) = f'(1) =

A: Given  f(x)=cos x-3tan x

Q: 2 Find the x-intercepts of y = 2 sin x + sin x – 1 on the interval [0, 27). %3D

A:

Q: If f(x) = 3 cos(5 In(x)), find f'(x). Find f'(1).

A: topic - derivatives

Q: Find the absolute extrema on the interval [0,2π] for f (x)=x/2+cos x.

A: Absolute extrema

Q: 11. Find if y= cos(x) A. 2x sin(x) B. -x sin(r) 12. Differentiate: y=x cscx A. y' = cscx(1+x cot x)…

A: we have to differentiate the given equation . y=ex3

Q: 22. y' = 1 + 3y tan x. ANS. 3y cos³ x = c + 3 sin x – sin³ x.

A:

Q: snip

A: Consider fx=sin x, gx=cos x. Evaluate: fg-1513. Let gx=y. y=cos x Replace y by x and x by y. x=cos…

Q: 21. If f(x) = (x² + 1) tan-(e*), then f'(0) = (A) 0 (B) - (C) (D) 1 e

A: It is observed that the function fx=x2+1tan-1ex is a product of 2 functions x2+1 and tan-1ex.…

Q: The function f(x) 22 e sin x+2x 5 cos x + has a removable discontinuity at a = 0. To remove the…

A:

Q: 3 sin x If f(x) then 1+ cos x f'(x) = f'(1) =

A: topic -derivative of a function

Q: 12. Given that V3 cos x = cos(-x), tan x= A 3. cos(f B V3 C 1. V3

A:

Q: i. f(x) = sin(cos(tan(2x))) j. f(x) = In³/2x

A: we have to differentiate it:-

Q: Given that f"(x) = cos(x), f'(x/2) = 4 and f(r/2) = 7 find: f' (x) = sinx+3 f(x) =

A:

Q: 25. Assuming that (d/dx) (sin x) = cos x and (d/dx) (cos x) = - sin x, prove each of the following.…

A: Our Aim is to prove the derivative of the following:-(i) ddxtan (x)=sec2 (x)Proof⇒ddxsin (x)cos…

Q: Find the points of inflection,smaller x-value,and larger x -value  of the graph of the function. (If…

A:

Q: 1. Determine the absolute extrema of f(x) = (sin x – 1) cos x on 2' 2 if they exist, and identify…

A: Given:-f(x)=sinx-1cosx,        x∈-π2, π2f'(x)=sinx-1ddxcosx+cosxddxsinx-1…

Q: If f(x) = 6 sin x + 10 cos x, then f'(x) = f'(4) =

A:

Q: If f(x) = 5 sin x + 2 cos x, then f'(x) :

A:

Q: Given f’(x)= 3 cos x - 9 sin x and f(0)= -6 find f(x)

A: We can solve this as follows:

Q: Which of the following is equal to f(x)dx where S(x) =- sin(x) if 0<x< a/2 l cos(x) if 1/2<x<a } -2

A:

Q: 2. If f(x) = 2x – 1 and p(x) = = cos (x). Find x, for 0 < x < 2n, if (f •p)(x) = -2

A:

Q: If y = sin (sin x) and d dy tan x + f(x)= 0, then f(x) equals dx2 (A) sin² x sin (cos x) (C) cos? x…

A: Introduction :

Q: If f (x) = - sin(x), then f (11) (x) is equal to A - sin(x) B - cos(x) sin(x) D cos(x)

A: Differentiate 11 times

Q: Given f(x) = x² +3 sin x+2 cos x. Find (f-ª) (2).

A:

Q: 2. For the function f(x) : = sin x. Show with the aid of the elementary formula. 1 1 (1- cos 2A)…

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Q: Find f'(x) for f(x) = sin?x · tan (x² – 3x + 1)5).

A: We will find the derivative.

Q: Find f(x), where f'(x) = sin(x) + cos(x) +1 and f(7) = 2.

A: Given: f'(x)=sin(x)+cos(x)+1 and f(π)=2

Q: If f (x) = - cos(x), then f (0)(x) is equal to A - sin(x) B - cos(x) В © sin(x) D cos(x)

A: We have to differentiate the given function 9 times

Q: (5) Find the local extreme values of the function h(x) = sin?x – V2 . sinx + 2/2 on the interval (0,…

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Q: Determine the extreme values of the function f(x) = 2 cos(x) –1 on the interval [0, 27].

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Q: If f(x) = 6 sin x + 12 cos x, then f'(x) = f'(4) = %3D

A:

Q: 1 The function (x) = x sin x satisfies the following equation: f"(x) + f(x) + t cosx = 0. The value…

A: solve the differential equation

Q: Determine the ABSOLUTE EXTREME values of the function y = cos x + sin x, over the interval 0<x < 2T

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Q: Suppose v is in the interval (G, T ), with tan v = –3 Find the exact expression for the indicated…

A: