Differentiate. sec(0) 6 + sec(0) f(0) %3D sec 0 tan 0 f (θ)- (6 + sec 0)2

Q: tan + x Anctan ly =0

A: The given differential equation is,

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Q: sec" y dy- (f) tan y

A: Topic = Integration

Q: f" (x) = cos x, f(0) = 1, f'(0) = 2, f'"(0) = 3.

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Q: Find the absolute extrema of the function on the closed interval. y = 5ex sin x, [0, π]

A: Solution:-Given functiony=5exsin x in [0,π]∴f(x)=5exsin xf'(x)=ddx5exsin x∴f'(x)=5ex cos x+5ex sin…

Q: sin (x + y) %3D coS Xcos y 7. tan x + tany

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Q: cos x 3. y = tan (3x)cot (3x) 4. y = 1+sin x 5. y = arctan (3x5) 6. y = x arcsin x + V1- x²

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Q: An equation for the tangent line to the curve In(sec x + y?) = tan(x)+e2" – 1 at the point (x, y) =…

A: Given curveIn (sec x +y2) = tan x +e2x-1We have to find the equation of tangent line at the point…

Q: FIRST DERIVATIVE: Two point central y = x + 4x – 15 at x = 0, h = 0.25 Your answer SECOND…

A: As per our guidelines I am solving only 1st for others kindly resubmit the question mentioning that…

Q: a) cot x – tan x sec x(csc x – 2sinx) %3D b) cor y(sec²y – 1) = 1

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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: 5. cot(2x)[2+csc(3x)] 0 x &R 6. tantx - tan2x=-V3(1+tan4xtan2x) xE[-n,"|

A: We have to find the solution in radian

Q: x cos'(y)dx + tan y dy = 0, y(4) = 7 2. X COS

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Q: Find an equation of the line tangent to the following equation at point x = 1. tan x f(x) =x What is…

A: Given : f(x) = xtanx

Q: I. Find dy -and simplify the result whenever possik dx 1. у%3Dsec3 2х - 3sec2x 2. y = sin (x + 4 )…

A: Given; 2) y=sin(x+4) cos(x-4) 3) y= -3 cot5(x/3)/5 + cot3(x/3) -3cot(x/3) - x.

Q: Prove the reduction formula

A: To prove: ∫tankx dx=tank-1xk-1-∫tank-2x dx

Q: sec 2x cos y dx + (cos 2x + cos 2x cot2 y) dy = 0 ans: tan 2x + 2 In |csc y - cot y| = c

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Q: Find y' of y = tan(x+1) %3D

A: Given: y=tanx+1x To find: y' Solution: Quotient rule of differentiation states that,…

Q: 2. Find the derivatives of the folowing equations: y = sin-'(1 -t) y = csc-(x/2) y = In(tan- x)

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

Q: y = tan In(x + sin x) %3D y = sin x + In sin e* %3D

A: y=tan ln(x+sinx) y=sinx+ln sinex

Q: (cos x cos y cotx) dx - sin x sin y dy = 0 -

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Q: Question 18 Find the derivative of y = tan (3x) [sec (2x)]-1 3 cos (2 x) – sin (6 x) sin (3 x) A cos…

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Q: 6) By implicit differentiation find a) xy + y² = 2 find d²y/ dx² %3D b) sin(x²y²)= x find dy/dx

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Q: 15. Find the derivative. (a) f(0) = arcsin 02 %3D (b) h(t) = arctan(e*) %3D

A: Given:- (a) f(θ) =arcsin(θ2)  (b) h(t) = arctan(et)  To find:- Derivative of given functions

Q: Cos z+1 cos 2 1 + sec x =

A: Use simple trigonometry relation.

Q: y + y tan x = cos x; y(x) = (x + C) cos x, y(n) = 0

A: Given that, y'+ytanx=cosx     ---1yx=x+Ccosx      ---2y0=π We need to verify whether equation 2 is a…

Q: y = In(sec x + tan x)

A: Solve the above differentiation.

Q: The surface of a water wave is describedby y = 5(1 + cos x), for -∏ ≤ x ≤∏, where y = 0corresponds…

A: Given- y=51+cosx and consider the figure, To find- The average height of the wave above the trough…

Q: (c) curve y = 5-x", line y=x+3 (d) y= sinx, y=cosx, x= 7 /4, x=7/2

A: Double integers

Q: 5. J 12 csc (-6х) cot (-6x) dx 6. J2x3 cot х4 dx 7. S xª sec (x5 - 9) dx 8. S tan 3 x dx

A: The given integral are 5) 12 csc(-6x) cot(-6x)  6) 2x3 cot(x4)

Q: (b) y=sec x, y = tan x, x = 0, x =1

A: Refer to the figure shown below:   The (grey) area bounded by the given curves is revolved around…

Q: 1. Integrate: Transformation by trigonometric formulas X x 1.1 sin sin dx 5

A: Use trigonometric identities,                                          sin2x + cos2x = 1

Q: Find y' given that y - y' sec²√x tan√x √x y' = 2sec√x tan² √x y' = 2tan√x sec² √x sec√x tan√x y' √√x…

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Q: (sin y- y sin x)dx + (cosx + x cos y)dy = 0

A: Disclaimer-Since you have asked multiple questions, we will solve the first question for you.  If…

Q: Solve (cos x cos y- cot x) dx-sin x sin y dy = 0 %3D

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Q: sin x sin y dx + cos x cos y dy = 0

A: Using variable separable method.

Q: f(x) = cos x + 3, [0, 27], midpoint

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Q: find 3 sec“ 3x dx sec4 0 do 41. 42. csc“ 0 do secó x dx 43. 44. 7/4 4 tan³ x dx 6 tan“ x dx 45. 46.…

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Q: 2. Function: y = 2 cos ( 2.5x +) 2n 3n 5n 3 4 6 0° 30° 45° 60° 90° 120° 135° 150° 180° 7n 11n 2n 6 4…

A: Let us find the amplitude, period and displacement of the given SHM in the next steps.

Q: Q3|A: Find ý if 1-y = cot vx +2 2- y = tan v+ Vtan x 3- y = tan x+ * cot v

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Q: 7 sin x Let f(x) 6 sin x + 2 cos x Then f'(x) The equation of the tangent line to y f(x) at a = -…

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Q: Find the directional derivative of f at P in the direction of a. f (x, y) = 7 tan-1 ; P(-8,8); а%3…

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Q: y = Arccot (cosx ) ; y' ' O sin x/ (1+ sin*2 (x) ) ) - sin x / (1+ sin^2 (x) ) ) sin x/ sqrt (1-…

A: Given y=cot-1cosx We will find y'that is the derivative of y. Chain Rule: If y=fgx, then y'=f'gx·g'x

Q: 2) + (2x tan-" y – x³)(1+ y²) = 0 Ans: tan-y=(x² + 1) + ce-*²

A: Bernoulli differential equation in the form of: dydx+k(x) y=q(x) yn 1yndydx+k(x)×1yn-1=q(x)…

Q: f. – 1 = tan 0 sec 0 over [0, 2n)

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Q: 3. sin x cos y dx + cos x sin y dy

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Q: (x - y sec2-x tan2) dx + x sec2 an²) dx + x sec² 2 dy = 0 x.

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Q: √x(y)²-(√x cos √x - sec √x)y'=1

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Q: 7. What is y' of the function y = arcsin V1-x |? Assume 0 <x < 1. C) y'=- Vx-. A) y'=-- B) y'= - D)…

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Q: +2e* +sin x)dx a. 3t + b. dt с. sec 0(sec 0- tan 0)d0

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