Verify the following sta 1 -1 tan dx x) = 1+x

Q: Compute the following derivative: tan e dr 30 – cos 0

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Q: Evaluate each of the following: csch (2 sin 2x)dx V1-4x 1. 2. 3.

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Q: Differentiate the following function COS T 1 (a) sec(x) tan(x) (b) (c) sin (4x° + cos(x))

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Q: cosx t cost (a) f(x) = (b) у %3D 1+ sinx 1-t

A: Follow next step

Q: Find each of the following derivatives: d arctan 1 – cos(2x2) 1+ cos(2x2) | • A = dx COS

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Q: Determine whether the statement (d/dx) [arctan(tan x)] = 1 for all x in the domain. is true or…

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Q: Integrate the following. - sec²x 3. ( sec?x tanx

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Q: FIND DY/DX OF THE FOLLOWING 3. y-tan (1+sinx)

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Q: Prove the following derivative statement. Include supporting mathematical statements within a…

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Q: Evaluate. sec?x tan x dx

A: As we know that the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1 From the given problem:…

Q: Find integral.

A: To Determine: ∫ e-xtane-xdx

Q: d (sec x) dx Prove that sec x tan x.

A: We have to prove that: ddxsec x=sec x tan x We know the formula of derivatives, dxndx=nxn-1d cos…

Q: Evaluate: [ cos 2x log(1+ tan x) dx

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Q: If f(x) = 5x(sin x + cos x), what is f'(x)?

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Q: S tan ( – y) dy 4

A: ∫tany4-y dy=∫tany-4y4 dy=∫tan-3y4 dy Now put, -3y4=t⇒-341=dtdy⇒dy=-43dt

Q: Find the function if sin t T+1 1 tan 2x + 1

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Q: Integrate the following. 3. f sec?x dx tanx

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Q: f(a) tan(x) + sec(x) simplifies to where cos(x) f(x)

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Q: Evaluate (a) ſ In(2x + 2)dx /3 (b) [ sec'3x tan 3x dx

A: Please see the answer in step 2

Q: Rewrite f(x) = 5 sin(3x) – 2cos (3x) in the form A sin (Bx + C). Round your final angle to two…

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Q: Write ∫ tan2k+1 x dx, where k is a positive integer, in terms of ∫ tan2k−1 x dx.

A: Given integral is ∫tan2k+1dx. Rewrite the above integral as follow.…

Q: prove that  d/ dx ( sec x) =sec x tan x

A: We have to prove ddxsecx=secx tanx We know that secx=1cosx So, we have to differentiate ddx1cosx…

Q: Let f(æ) = - 6 sin(x)cos(x). %3D df dx d²f da?

A: Using product rule, (uv)'= u'v + v'u Here we take, u = sinx v = cosx df/dx =(uv)'…

Q: Using an appropriate substitution, S tan (x)sec (x)dx is equal to:

A: Given∫tan3(x)sec9(x)dx

Q: tan x sec? x dx

A: Given integral: ∫tan2 x sec2 x dx

Q: B. Evaluate the following 1 dx 2. 2 tan(x)dx 3.

A: We have to slove above question

Q: Find f'(x) where f(x) sin(cos(4x2 +1))

A: Consider the given function

Q: Evaluate tan-1 x dx 8.

A: We have to evaluate the integral: ∫-∞∞tan-1xdx

Q: Assume sin(t) = -12 where π < t <3. Compute the following: csc (-t) = cos(t + 2) = tan(t) =

A: We have given  Sint = -1/12 , where π&lt;t&lt;3π/2  Compute  1) cosec(-t)  2) cos(t+π/2)  3)…

Q: (a) Show that tan x = dx sec?x using quotient rule.

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Q: If f(x) = 2x(sina + cos a), find f'(x) = %3D

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Q: d Prove that sec x tan x. sec x dx - 3.

A: Given that

Q: Use the Reduction Formula to evaluate the following (a) f sin“ x dx (b) S tan x sec4 x dx

A: (a) The reduction formula for ∫sinmxdx is given as the following.…

Q: Evaluate si (z* - tan(z) cos(z) ) dx 2-1

A: To find the integral: ∫11x2-tanxcosxx3-1dx

Q: Differentiate the following function f(x) = sin(sin(v2x)).

A: Differentiate the function  f(x)= sin(sin(√2x)) .

Q: Evaluate the following indefinit 4. Ssin'x cos*x dx

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Q: 4 (tan(sec(x)) d

A: Recall: df(g(x)dx= f'(g(x)) g'(x)     Chain Rule Differentiation d(tanx)dx =sec2x d(sec x)dx =secx…

Q: Express the following as an algebraic function of x. sin(sin¯ (x) – cos-'(x)

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Q: d (sec x) dx 18. Prove that = sec x tan x. %D

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Q: If g(x): = cos 2x and f(x) = sin-n, find g(f(x)). %3D

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Q: Find the following integral:

A: Use substitutions to integration

Q: Evaluate Te*(sin x +cos x)dx

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Q: Show that tan(arccosx) for |x| s 1, x + 0.

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Q: Jse graphs to evaluate sin x dx and coS x dx.

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Q: 1. Differentiate each function by using formulas. t cost (b) у %3D COSX (a) f(x) = 1+sinx

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Q: Differentiate each of the f cosh(x)+1 cos(r)+1 a. Y =

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Q: Differentiate the following x 2 tan(y) + y 10 sec(x) = 2x

A: Given that

Q: "/3 tan5x sec²x dx

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