Question 5 (1 point) The derivative of y tanh(In x) is -4x Oy = x²+1 -sech? (In x) Oy = 4 Oy = x(x+)* ' Oy sech (In x) x In x None of the above.

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A: The given differential equation is,

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A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: 4. y = 5 cos 4x, 3rd derivative 5. y = 3 tan 3x, 2nd derivative %3D 5. y = 6 csc x, 2nd derivative

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

Q: HR MIN SEC n6 of 6 Calculate the first, second, and third derivatives of 12 y(x) = 42+x (Use…

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Q: 2. Find the derivative. Simplify where possible. (b) у %3 tanh-1(г3)

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Q: 8) (10 points) Use Integration by Tables (Appendix B) to find the integral: sin 2x dx 5+3 cos x

A: Explanation of the solution is given below...

Q: 3) f(x) = ln(x5 - cos²x) 5) f(x) = xsinx 4) f(x) = x² 1 + x³ 1 6) f(x) = x¹ tan- X

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Q: 1 -dx cos.x-1 2) Integrate

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Q: lim h-0 2h sin(x² )dx = -2h cos(1) sin(1)

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Q: ) Prove that tanh'x = tn/itx, X€ (-1,1) i) , Sinh 'x and tanh'x Find the derivative of coch'x

A: (1). We have to prove that:   tanh-1x=12ln1+x1-x

Q: 1+sin 2 x 1) Find the derivative of f(x) %3D 2 cos3 x

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Q: 6. Find 39th derivative of f(x) = sinh(x). A. sinh(x) B. cosh(x) C. – sinh(x) D. - cosh(x) None of…

A: Derivative of sinh(x) is Cosh(x) and  Derivative of Cosh(x) is Sinh(x).

Q: (8) Find the derivative of the functions (i)h(x) = sin 2.x cos 2x (ii) f (x) = cos (tan 4.x) 1 =-…

A: We need to differentiate the given function. We will use different method of differentiation . ( As…

Q: 15. sinh 2x = 2 sinh x cosh x %3D

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Q: 1-sin(x) (1-Sinx)2 10. Find the equation of the line tangent to the graph of y = 3cos(x) at the…

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Q: Question 5. (i) Explain why there is no value of a which satisfies the equation cos t dt = sin x +…

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Q: sinh x + cosh x)ª= e4x

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Q: Find the derivative of y = tan 1 1-x -1 + sec Va +1

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Q: S(sec x tan x – 4x³)dx = - o tan x + х* + с sec x x4 + c sec x + x4 + c - sec x + x* + c - sec x x4…

A: Some of the properties of integration ∫f(x)+g(x)dx=∫f(x) dx+∫g(x) dx ∫xn dx=xn+1n+1+C ∫ (sec x tan…

Q: a) y = In x · sinh x*

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Q: tan y-1 . sin y- cos y- 1 www. Prove that tan y +1 sin y + cos y+1 2.

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Q: 4. The 1" derivative of y : cotx a) xsec?x + tanx b) xsecx - tanx c) cot x + xcsc'x d) cot x - xcscx

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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: 1+sin 2 x 1) Find the derivative of f(x) 2 cos3 x

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Q: Example 17: Find the derivative of function g (t) = tan (5 - sin 2t). Solution: %3D Notice here that…

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Q: 7. y= (x²-1) sinh (x+1)ª 8. y= sech (1-x³) 9. y =- tanhx

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Q: (5) sinh 2x = 2.sinh x.coshx %3D

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Q: sin 0.5 va Find the first-order derivative of y = at x = 2 and h = 0.2 a.) Forward difference b.)…

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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: 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: 9. Solve 4(sec² x)(3 – tan x)/2 dx by substitution. Remember that the first derivative of tan x is…

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Q: cos*(x)dx

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Q: verify that sinh x and cosh x are derivatives of each other. Verify: (cosh^2)(sinh^2) x = 1…

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Q: 1.Find the derivative of the function y = cosh*x – sinh“ x - 2.Find the derivative of y = In cosh x.…

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A: topic - derivatives

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Q: ∫(3 cos(x) − 7sinx(x))dx   Evaluate indefinite anti-differentiation

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Q: 1. State the power rule. 2. For which values of n have we proved the power rule? 3. Based on your…

A: 1. The power rule of derivatives gives the following: For any real number n,      ddxxn=nxn-1