Hiw/ Find F'(x) 1. if F(x) = x, tanx 2-if y = Sinx it casx 3- Find g" ()if y co) = Sec y ex) g ex) =Sec 3-

Q: 4. Find using derivative rules. dx sinx x8+x x2 tanx (a) y = (b) y= (c) y = cos³(3x² + 9) cos(5 x*)…

A: As per our company guidelines, we are supposed to answer only the first 3 sub-parts. Kindly repost…

Q: y=8sin(x)cos(x) ; x=pi/3

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Q: If x+y divided by x-y= x^2+y^2 and dx/dt=12, then what is dy/dt when x=1 and y=0? show all work…

A: Given thatx+yx-y=x2+y2x+y=(x-y)(x2+y2)  [cross multiply]x+y=x3+xy2-x2y-y3

Q: 7. Find the derivatives of y = cos- (sin(2x)) (show work)

A: Using derivatives of composite function. Or Using trigonometric transformation.

Q: |2tan x In (cos x) dx=

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Q: 4. Find by implicit differentiation of x sin(y) = y cos (x) dx

A: The given problem is solved below in detail.

Q: 6. Find dy/dx by implicit differentiation for tan-'(²y) = sin(x²) + 3ry?.

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Q: Find the derivative of y with respect to x. 2x + 3 26) y = sec = sec-1 27) y = -sin-1 (5x2 + 2) 28)…

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Q: 1) Find 4 by implicit differentiation given 4 cos x sin y = 1. dx

A: Differentiate above equation with respect to x.

Q: 2tan x In (cos x) dx=

A: here we have to integrate the given integral.

Q: If given integrand is x² cos 2x dx and dv is equal to cos 2x dx, what is v?

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Q: Limit as x approaches 0 1-cos(x)/sin(x)

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Q: 28. The derivative of In(x sin x) is 1. 1 + cotx а. b. C. d. tan x +x - +x sinx

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Q: Find the x values of all the horizontal tangents to the function f(x) = cos.x + /3 sinx on the…

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Q: Find an equation of the tangent line to y sin 2x = x cos 2y at the point π/2 , π/4 . Do not…

A: First we will find Differentiation of given equation to get slope of the tangent line. Now equation…

Q: d arctan (tanh x) dx Show that sech 2.x.

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Q: Find the derivatives of the functions in Exercis

A: Chain Rule: f(g(x))'=f'(g(x))g'(x) Differentiation formulae: ddxsinx=cosxddxcosx=-sinxddxax=a

Q: f y=sin(sinx) show that y'' +(tanx) y''+y cos2x=

A: Given that y=sinsinx To show that y''+tanxy'+ycos2x=0

Q: Find the derivative. y = sinh 1(tan x) O y = |cos x| O y = 1 /1+tan x O y = 1 Vtan? x-1 O y = |sec…

A: In this we have to find integration and derivative.

Q: Find the derivative of y with respect to x. y= 3x^3 sin^-1 x show all work

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Q: Evaluate: S Arctan 2 sin²x dx . Arctan 1 cos+x

A: Given,  ∫Arctan1Arctan2sin2xcos4xdx

Q: Determine whether f(x) is differentiable at x = 0. Show your work. sin(x) cos(x)-1 3x + 1 f(x): = if…

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Q: )if x+tany+ sin-x+ In(yx) +3**1 =4 then find y'

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Q: Find the first derivative of y = arctan [ (3 sin x) / (4 + 5 cos x) ] and y = ( ex – e –x ) / (ex…

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Q: 1+ tanx y = logy 1- tanx prove that 9 = sec2x dy dx

A: Given,           y=log1+tanx1-tanx

Q: The second derivative of y = ln(sec x) is а) у 1 - tan x b) y = tanx sec x c) y = secx · tan x d) y"…

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Q: If tanh(x) = 24, find the values of the other hyperbolic functions at x. sinh(x) %3D cosh(x) coth(x)…

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Q: Find the equation of line tangent of sin(2x) cos(3x)+ sec(x) TC At x = 6. %3D

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Q: What is the second derivative of ecON (), , Cosh (A sinh?(x)e cosh (x) + cosh2(x)ecosh («) B sinh…

A: Let the given function is y=ecosh(x).

Q: 57 ves y sinx and y=cosx from x=- to x=- 4 4

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Q: y = In(x² + 4) - x tan-1 (e) y = arctan(arcsin vx), (y = sech (tanh x)

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

Q: 4. Ify =/sin x+ /sin x+.to inf inity, dy _ cosx dx 2y-1 prove that

A: Derivative of Sinx is Cosx

Q: Find* esin ¤ dx tan x csc x cos x e $in xt. - cos x e Sin x + c Option 4 Option 2 esinx + c ,sin.…

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Q: Limit _π/2 toπ/2 integral (1+cosx) dx

A: To integrate: ∫-π2π21+cosxdx Solution: Property of definite integral states that: ∫-aafxdx=2∫0afxif…

Q: ind the equation of the line that is tangent to y = 2x + sin x + cos x at x = 0.

A: NOTE: Refresh your page if you can't see any equations. . take x=0 the point on the graph is

Q: Find the first derivative of  y = cos4 x – sin4 x y = x3   –  x2 cos x  +  2x sin x  + 2 cos x y…

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Q: What is the second derivative of y + Incosx = 0 * O (cos x) ^2 O 1 O (sec x)^2 tan x

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Q: Q3- Find: 1- Sv2 + sin3x . cos3x dx. 2-5* dx x5-2x sin 2x 2 sin x 4- f cscx cot x dx 4 cos x 5- S 3+…

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Q: Prove dx dx 1 f ( sec -x+tan –I 2 1 | f (cosecz) %3D Vsin r sin x

A: Apply trigonometric properties to prove the result.

Q: sinx f(x) = on [0, 2n] cos x-V2

A: Given :         f(x) = sin xcos x - 2 on 0, 2π   To determine the extrema of the above function…

Q: Find all points with x-values on (0, 2π), where tangent line to the graph of f(x) is horizontal.…

A: Find all points with x-values on (0, 2π), where tangent line to the graph of f(x) is horizontal.…

Q: 1: Find the derivatives of: 1+ tanh x a) y = In ソ= %3D 1- tanh x b) 2 y= cosh? 1-x? 1-x

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Q: Find the derivative dy/dx of y = cos 3x O 3 sinx О З cosx O 3 sin 3x О З сos 3x none of the above

A: We can do this by doing derivative both side.

Q: 1. Find the point(s) if any where f has a horizontal tangent line. у %3D УЗх + 2 cos x 0<x < 2п

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Q: 3 cos x Evaluate | dx by using substit ution method. (1+sin x)“

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Q: find tan x dx x² x² tan¬' x dx 19. 20. sin 3x cos 2x dx 22. sin 2x cos 3x dx S sin sin 8 sin 4t sin…

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Q: Compute cosh(x) and sech(x), assuming sinh(x) = 0.01. cosh(æ) = %3D sech(x)

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Q: limit x approaches zero, sin^2x/x

A: Given,

Q: Find when 4= SINX Thuen dy (sinx) (ar f(s wheve for 0<x< M2 tanx taux a=?

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