Evaluate / x. sec² 2x. dx. x.tan2x + + ilog(sec2x) + C 2 O log(sec2x) + C O None xan - log(sec2x) + C

Q: Compute the derivative.    f'(3),   f(x) = log5 x

A: Given: fx=log5 x  ……1   To find: f'3

Q: take natural log from both sides and solve the right side using the log rules. Then, take derivative…

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Q: Find the first derivative: y = 3 arcsin(cos 2x) %3D O-7 O -8 O -4 O-6 O-5

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Q: Graph the defined function over a one-period interval. y = - sin (x - pie/2)

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Q: Differentiate: (etan(x)) /(1+x)  Show all working out.

A: Given  etanx1+x. We have to differentiate it. Used formula:- ddxfxgx=gx⋅ddxfx−fx⋅ddxgxgx2 Here,…

Q: Evaluate cosh #j in 3 decimal places.

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Q: ln(x) is just defined for x greater than 1. Select one: True False

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Q: Compute sinh(ln 5) and tanh(3 ln 5) without using a calculator.

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Q: Find the root of the function using Fixed-point Iteration. f (x) - x cos (x) - x?

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Q: 1- Prove that cosh 2x - sinh 2x = e2

A: sol)Given cos h 2x-sin h 2x=e2x

Q: tion of all components of v(3) correct to two decimal places.

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Q: Compute the derivative. k(θ) = θ2 sin2 θ

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Compute : , log,(cosx) d dx - sin x A. (In 2). cos x 1 B. (In2).cosx -(In 2). sin x C. COS X -In2 D.…

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Q: 2. Compute for a real root of sin -x 0 using three iterations of Fixed- Point Iteration Method with…

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Q: sinh(9x) If g(x) : 8 + cosh(9x) find g' (x) 8+ cosh(0)

A: Following formulae are used to solve first question

Q: tan s) Differentiate f(x) = 5* log3 %3D csc 2x

A: Consider the function fx=5xlog3tan-1xcsc2x Here, the objective is to differentiate the function.

Q: 9 coshx - 5 sinhx = 15

A: Note the following result : cosh x=ex+e-x2  sinh x=ex-e-x2 . In above formula , x∈ℝ . To solve the…

Q: Differentiate  f(x)  = log 10  ( 2+ sinx )

A: Rewrite the given function as shown below: fx=log102+sinxfx=ln2+sinxln10        since logab=lnblna

Q: What is the first derivative of q(x)=(3x)7x at x=2?  Enter an exact answer in terms of a natural…

A: When there is variables in exponent we should take log both side then differentiate. Here we use…

Q: dr 3. Verify that = ln(2). x(x+1) 1

A: Given: ∫1∞dxxx+1=ln2

Q: : Find value of x if :- 2 sinh (2x) - 4 cosh (2x) = - 4

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Q: Use false position method to find the root of f(x) = e* (3.2 sin x - 0.5 cos x) on the interval…

A: We need to find the root of fx=e-x3.2 sin x-0.5 cos x The given interval is 3,4 Also, we are…

Q: Compute coshx and tanhx, assuming that sinhx = 0.8.

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Q: 2. y=cot1-2x 3. y=log22x*

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Q: logtan nx(2+ 4 cos nx) 2

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Q: Verify the identity. sinh2 x = (−1 + cosh 2x) /2

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Q: Verify the identity cosh 2x = cosh2 x + sinh2 x

A: we have to verify the identity: cosh(2x)=cosh2x+sinh2x   L.H.S: cosh2x as we know that coshx=ex+e-x2…

Q: (7) Find if \.Y =ln12- Cosx) , 2- Y= %3D

A: Calculate dydx. 1. y=ln 2-cos x. Derivate with respect to x by applying chain rule: dydx=dydududx.…

Q: Prove the identity arcsinhx=ln(x+√1+x2).

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Q: Verify the identity by transforming the lefthand side into the right-hand side.

A: Consider the given equation. logtanθ=logsinθ-logcosθ Take all the value right side of the equation.…

Q: Use a calculator to compute sinh x and cosh x for x = −3, 0, 5.

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Q: Find dx 1- y = log (Sin x )- Cot - Vx 3 2. y = log( vx) = tan(x - y) 3- x Sec -x = y? log (sec x) 4-…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 1. f(X)= xpi - pi(x) + pi/x + pix - cos (pi)

A: Given, fx=xπ-πx+πx+πx-cosπ We know that dxndx=nxn-1daxdx=axlnx

Q: Q5: Evaluate : 3 1- Domain of:- log10 (x-x) 2- Rang of : cosx – sinx 3x +3y = 28y (3x+y = 27 ) %3D…

A: Domain of log(x) is x>0.

Q: If f(x)-logCos4x + sinx.Then find 9 (x) JP at x= sec 2c dx 6.

A: Given function is: f(x)=logsec2x|cos4x|+|sinx| To find the value of 9df(x)dx at x=-π6

Q: Find the derivative of ƒ (x) = cos-1(In(4x²+1)).

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Q: * limt (x-sinx)\ x+1 10 log x^2+3 O 0.5

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Q: 3. Use Log Rule to integrate. J6x-5 dx a. 6х-5 b. S- 1 dx x Inx

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Q: 1- Y= sin( coshx log2 2 ) 2-Y= sinx.coshx. log2 2 3 - y = In Vx. sin x

A: Apologize  that we are permit to do first question of the multiple questions but still I am doing it…

Q: (b) Prove that : - 1) (coshx)2 - (sinhx)2 = 1 ,2) coshx - sinhx = e, 3) (cothx)2 -1= (cschx)2 %3D

A: Use hyperbolic  function

Q: Evaluate /(e* + - + cos4x)dx O + logx + sn3x +c e2r 3 4 e3x sin4x + logx + + c 3 2 O + logx + e5x 2…

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Q: Use logarithmic differentiation to evaluate ƒ′1x2.  ƒ1x2=11 + x22sin x

A: Given: fx=11+x22sinx

Q: if 2 tanh x.In x = sinh' (sin x)+logcos dx dy Q5/ Find

A: To differentiate the given function.

Q: If g(x) : 8 + cosh(9x) find g'(x) 8+ cosh(0)

A: Answer and explanation is given below

Q: Evaluate ax xm-1 sin bx dx in terms of Gamma function. -ax

A: We use the special results of Gamma function to solve this problem as in next step.

Q: Use definition of hyperbolic function to prove that 2 sinh x cosh x = sinh 2x. Hence, solve the…

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Q: Find the derivatives of x log x.log(logx)

A: We have to find the derivative of-  x logx.log(logx)

Q: To evaluate the integral cotx log(sinx) dx we use the substitution O a. sinx=t O b. logx=t O c.…

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