Example 6: Differentiate (a) y= sin(x²) (b) y =sin (x) %3D (c) y= e*cc30 (d) y=tan(4.x² –1)

Q: Differentiation#11

A: We have

Q: 1 lim h-0 2h sin(x²)dx = %3D -2h O cos(1) sin(1)

A: Using Fundamental theorem of calculus: ∫-2h0sin(x2)dx=sin(0)-sin((-2h)2)=0-sin(4h2)=-sin(4h2)

Q: 18) e2x = sin(x + 3y)

A:

Q: s sin² (3x) cos³ (3x) dx Hint: cos²x = 1 - sin² x 07 sin²x = 1 - cos² x

A:

Q: : / ain(tun3x)dx cos²3x tan( tan3x) dx Evaluate: A -in|sec(tan3x)| + c 3 B 3 -In|cos( tan3x)|+C O…

A: On solving this we will get

Q: 3+9sin' x Evaluate dx using suitable technique. cos x

A:

Q: cos^2ydx+(1+e^-x)sinydy=0

A: The given differential equation is cos2ydx+1+e-xsinydy=0.

Q: sin(4x) cos(2.x) dx n (2x) sin (6x) cos (2x) cos 2. ()= 4 'cos (2x) cos (10x sin (2x) trts 10 (e)…

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Q: Example 1 Find dy/dx, if sin (²+3x+¹) b. y = cos²(2x-1)

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Q: coS x dx 6) 1 + 3 sin x A) In| 1+3 sin x|+C C - 를 In| 1 +3 sin x| +C

A: To evaluate ∫cosx1+3sinxdx

Q: y= sin(x + 4) cos (x - 4) y= sec 4x + tan 4x y= Arctan

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: sin(4x) cos(2x) dx = cos (2x) cos (6x)' sin (2x) cos (2x) сов (10х) 4. (2x) sin (10x)+ c sin +c 10…

A: Use formula 2sinAcosB=sin(A+B)+sin(A-B)

Q: ¥2/3 6. cos'x sin x dx 5.

A:

Q: 1) "(x - 2 sin(x))dx. 4+x² 2) ** dx. dx 3) S cos?(x) 1+tan(x)

A: To evaluate the integral.

Q: Find the solution of (tan x – sin æsiny) dæ +cos xcosydy = 0

A:

Q: 2. 1- x2dx cos(x + 1) dx 3.

A:

Q: 1. Solve the DE tan x sin y v + ( 3tan X -2 cos y) sec'x=0

A:

Q: 5. Let F(x) : = a sin(3.x) + bx cos(3x). Find constants a, b such that F'(x) = 2x sin(3x) and verify…

A: The detailed solution is given below Thank you

Q: elin (sin x+ cos x) dx 1. S ecosx

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: S cos ( x^3 ) dx = * sin ( x^3) + c 3x^2 sin (x^3 ) + c - sin (x^3 ) + c - 3x^2 sin ( x^3) + c none…

A:

Q: O tan-()+ -dx =| Business Mathematics And Statistics x4 +1 Questions 1 O tan-(+e -) + c V2x x2 +1 O…

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Q: 19. -π/2 21. -π/4 23. [³5e* dx sin 0 de cos x dx sec² 0 do (2x secx tan x) dx 20. rπ/3 22. 24. [¹-dx

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Q: Q-6: Evaluate the integral 1). dx So Jie-1

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Q: 6 Evaluate (a) [ a + (4x-2° dx + (4x-2)* dx (2x-3)2 2x sin (x²+!) cos (x+1) dx

A: AS mentioned by you that "none of these is graded please answer 5. These are practice questions"…

Q: y = e2* (c, cosx+ c, sin x)

A:

Q: EXAMPLE 7 Finding Differentials of Functions (a) d(tan 2.x) = sec² (2.x) d(2x) = 2 sec2 2x dx (x +…

A: (a) dtan 2x=sec22xd2x=2sec22x Hence the answer.

Q: 2+ cos (1 + x»'½) .0.5x dx 22 cos (1+x³/2) V1+0.5 sin x 2,0.5x dx|

A: By using Simpson/Trapoizodal rule.

Q: Example 2: find ỹ,y=sin-1 Vx.sec-1 (sin x) Example 1: find ỹ,y=tan-1(x². sin x) Example 3: prove…

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Q: (3 tanx-2 cos y)sec" xdx + tanxsin yay = 0

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Q: 1. Solve the DE: (cos y- cos x)y' +cos y sin 2x = 0

A:

Q: 1. S(tan -1) dp 2. sin2 B cos ß dB 3. S: xdx -7-8x-x

A:

Q: EXAMPLE 2 Differentiate (a) y = sin(x³) and (b) sin3(x). SOLUTION (a) If y = sin(x³), then the outer…

A: Given:-(a) y=sin(x3)(b)y=sin3xwe have to differentiate(a) y=sin(x3)differentiate with respect to…

Q: 3. sin 8x cos 8x dx s 2x sin 2x dx cos

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Q: 4. y = tan(x+ a), 5. y = Aex + Be2x, 6. y = A sin 3x + B cos 3x, ,where A and B are arbitrary…

A: According to bartleby guidelines when student ask multiple subpart question then expert must have to…

Q: (1) x(x + 2)² dx x-x² (3) 4+x² dx e²x (2) 2) 14+720x dx J ex (4) | sin³2 sin³2 x sin 2x dx

A: According to bartleby guidelines when student post more than one question then expert must have to…

Q: 6-16 Find dy/dx by implicit differentiation. 6. 2x² + xy – y² = 2 10. хеУ — х — у 12. cos(xy) =1+…

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Q: sin 3x dr + 2y cos* 3x dy = 0 COS

A:

Q: 3 In(1+ V sin²x .limr→0 V1– cos x

A: Consider the given expression. limx→0ln1+sin2x31−cosx Put the limit in the expression.…

Q: cos (5x)cos (3x) dx cosh' (In x) sinh (In x) (A) (8) - (C) 0 (D) 2 1

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Q: 4 cos °x sin x dx 3x sin: 1/3

A:

Q: 1 a) 1+ sin(x) xp- Vtan (x)dx

A: a) Given integral is ∫11+sinxdx

Q: 6 (A) /₁ √== B)/ -x/4 D) dx = tan* (x) sec²(x) dx = C) [rea *² x² ex dx = E) 2x cosh(x²) dx = F) /…

A: Since you have posted multiple questions. As per guidelines we"ll solve only first question. If you…

Q: cos x sin x dx 4. sin 2x cos 2x dx 5. cos x sin* x dx 6. sin 3x dx 7. sin³ x cos? x dx 8. 3.

A:

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: y = sin(2x) sin(x) + cos ( 2x) cos (x) COS %3D

A: Using the formula of cos(A-B)=cosAcosB+sinAsinB. Explanation is given below..

Q: Example 1 Find dy/dx, if a. y=sin(x² + 3x + 1) b. y = cos² (2x-1)

A: I have stated the used formulas in the solution

Q: Example B Consider the inhomogeneous equation Yk+1 – 2yk coS Ø + Yk-1 = Rx, sin ø # 0, %3D

A: Given           yk+1-2ykcosϕ+yk-1=Rk  ,  sinϕ ≠0       ... (1) where ϕ is constant and Rk is…

Q: Q-1: Integrate the fraction of functions: 1. f- 14a+1 2. sinx- V(1-x) 2-7x-4x2 dx 3. SE 1-sine dep.…

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Q: (1) ſ [ (x³ + 2 + 7 ) dx (3) cos³x dx (2) √ x³ (2) x3 e3x+1 dx (4) sin x sin 2x dx

A:

Q: (x2+ 1)(x tan 8 dx 81. dx 3) (x+2)3 dx (sin (sin (e*))) 83. (In (sec x tan x)) dr dx xex P (sin…

A: We’ll answer the first question since the exact one wasn’t specified.Please submit a new question…