)etan²x f'(x) = (tan² x)et %3D Option 2 g tan?x f'(x) = (2 tan x)e

Q: 1. Integrate: [x³ sin(2x) dx.

A: As per Bartleby guideline, only the first question has been answered. If you want to get the answer…

Q: The first derivative of y = cos(3x-8) is O a. - sin( 3x-8) O b. 3 sin( 3x-8) O. - 3xsin( 3x-8) O d.…

A: Given function is, y=cos3x-8.   It is differentiated as follows: dydx=ddxcos3x-8

Q: (5x) S sin(x) tan(x) .........

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Q: Find the intergration of x^3(x^4-sine)^5 dx

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Q: find f'(x) if f(x) = tanh(ln x) +sin2(2x)

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Q: Evaluate S sinh x cosh x dx by introducing u-sinh x

A: Given that: ∫sinhx.coshx.dx

Q: 5. Integrate: [tan(7x)dx

A: 5) The given integral is ∫tan7xdx

Q: Find the derivative of f(x)=sin sin(5x

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Q: Use integration by parts to verify the reduction formula.

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Q: Integrate: S tan (æ) sec³(x)dx

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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: 1) [(sinh 2x + cosh2x)° dx

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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: integral of sin^5(3x)cos^3(3x)dx

A: The integral of ∫sin5(3x) cos3(3x) dx is sin5(3x) cos3(3x). If we need to find the integration then…

Q: 4. S(cos 2x)e$in 2.x dx 5. S cos x In(sin x) dx 6. ſ tan 0 In(sec 0) de

A: According to given : Only 4,5,6 are solved

Q: Integrate tan -1 x dx without using integration by parts.

A: We will find the solution in the following step.

Q: Evaluate S sinh x cosh x dx by letting u=cosh x

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

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Q: derive ^x dx cos"x Sinx + n-1 Cash Cos"-2x dx n-2, X. Jos"x dx in

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Q: 4. If y = x cos x determine the 5th derivative. [y(5) = (60x – x³) sin x+ (15x² – 60) cos .x]

A: To find out the fifth derivative.

Q: x/2 | (cos(x) + sin(2x)) dx of

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Q: 6. y%= arcsin a Va2-x2

A: Given: 6. y=xa2-x2-arcsinxa

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(t) = In Itsinx 1-sin x g(x) = x sin ¹3x + √1-9x² G(x) = x In (9 + x²) + 6 tan-¹ (-)-2x

A: Note: Since, in the first function there is a typing error "f(t)", it should be "f(x)" because it is…

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: Show that d /dx  arctan ( tanh x ) = sech 2x

A: We have to show that ddx(tan-1tanhx)=sech2x

Q: Find integration + dx Cos (x-1)

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

A: Given,           y=log1+tanx1-tanx

Q: 1. S cos (3 sin x)cos (4 sin x). cosxdx sec*x dx 2. Jtanx 3. Sr 6 tan*x dx 4. /2 sin5x dx

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Q: sinx 3. f(x)=(x)*

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Q: find integral sec 3 x dx

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Q: Compute sin x dx er + 3e -x 8.

A: We have to compute the given expression ∫sinxex+3e-xdx from -∞ to ∞ Therefore, The  given expression…

Q: 3. J sin53x dx. 4. J tan 2x sec22x dx.

A: ∫ax+bn dx=1aax+bn+1n+1+C

Q: 8. The value of f sinh* x cosh³ x dx

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Q: First and second derrivative of: y=5 /(sin 3x+cos3x)

A: the given function is: y=5sin3x+cos3x we have to find the first and second derivative of the given…

Q: Va2-x² Y=Arc sin + а

A: Differentiate wrt x

Q: 9. tan 4x sec24xdx d. cos 5xsin 5xdx e. x sin(3x² +1)dx f. [x* cos(2x' +1)dx

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Q: Find cosh æ In(sinh x)dx.

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Q: Find:  ∫cosh^4 (x) sinh^5 (x) dx.

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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: y=ln(sin(X3-1))

A: Detailed explanation is attached below.

Q: show that d/dx arctan (tanhx) = sech (2x)

A: On differentiation, we get

Q: 4. Use implicit differentiation to find az in xexyz sin(2z) – xyz = 5. ду

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: limit x to 0 3x-3xcox/sin^2(3x)

A: Here given limit as Use the L'hospital rule which states

Q: Va2-x² Y=Arc sin- + а

A: Solution-

Q: 4. S tan x dx CSC X sec (In x) dx 5. dx 6. S; 1- cos 2x

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Q: second order derivative of (5 sin 3x+cos^2 (3x )) is *

A: The function: y=5 sin3x+cos23x

Q: 1 Integrate: S tan*÷x dx 3

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