05 of the ac 42. Use the identity sin 2x = 2 sin x cos x to find the derivative of sin 2.x. Then use the identity cos 2x = cos x - sin?x to express that derivative in terms of cos 2.x. Idde

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

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Q: The derivative of any constant is 0. The well-remembered triq identity tells us that sin2(x) +…

A: To verify that sin2(x) + cos2(x) is a constant, we need to show that the derivative of sin2(x) +…

Q: Which of the following is the derivative of the function g(0) = cos(0) – sin(0)? Ogʻ(0) = cos(0) +…

A: Derivative.

Q: Derive the following function 8. y = tanh-1(sinx)

A: We have to find  the derivative

Q: What does the following identity tell us about the derivatives of sin -1x and cos- 1 x?…

A: Explanation: Suppose that,  A=sin-1xB=cos-1x   Now we can say that,  sinA=xsinB=x  So,  x=sinA=sinB…

Q: Express the given expression as a function of cos x. cos x + cos 3x cosʻ x – sinx

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Q: Find the linear approximation of f(x) = cos(x) at x = * and use it to approximate cos(134°). Give…

A: The formula for the linear approximation is: L(x)=f(a)+f'(a)(x-a) Here, given function is…

Q: 43. Use the identity cos 2x = cos x cos x - sin x sin x to find the derivative of cos 2.x. Express…

A: cos2x=cosxcosx-sinxsinx find the derivative of cos2x So here use product rule and then find…

Q: Which of the following is not equal to the derivative ofy = (cos(x) – sin(æ))= A 2 (sin? (x) – cos²…

A: The given function is y=cos x-sin x2

Q: Given the function f(x,v) = *ye6-sin²x e cos?x The second derivative f, of f is equal to 0. Select…

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Q: Find the derivative and show your complete solution of the following 1. cos(e ^ (2x) + e ^ (- 2x))…

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Q: In the given question, verify the identity:- sinh(x + y) = sinh x cosh y + cosh x sinh y

A: Consider the provided identity, sinhx+y=sinhx coshy+coshx sinhy Verify the provided identity.…

Q: 3. Compute 4 (sin? x + cos? x) without using the derivative formulas for sin x and cos x.

A: Given:

Q: (3) Estimate the error involved in using the approximation cos x = 1- for |x| < 0.01

A: To estimate the error involved in using the approximation cosx≈1-x22 for x≤0.01 The Taylor series…

Q: Use the addition formulas for sinh x and cosh x to prove tanh u + tanh v tanh(u + v) = 1+ tanh u…

A:

Q: Consider the function f(x) whose second derivative is f''(x) = 9x +8 sin(x). If f(0) = 4 and f'(0) =…

A: Recall: ∫xn dx=xn+1n+1+c ∫sinax dx=-cosaxa+c ∫cosax dx=sinaxa+c ; where 'c' is an integration…

Q: The derivative of y = 3 cos (V1-x²) + (1-x²), can be written as sin ( V1-x² ) – ( 1–x²) }) 3x…

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Q: 4. Use the inequality | sin r|< |x| for x E R to show that the sine function is continuous at r = 0.…

A: Sine function and it's continuity at 0

Q: (b) Use the graph of cos x to determine where cosx is positive and where it is negative. (c) Explain…

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Q: If x is in radians, the derivative of sin(x) is cos(x). Find the derivative of sin(x) when x is in…

A: Given, sinx°  We have to find the derivative of  sinx°.

Q: Consider the function f(x) whose second derivative is f"(x) = 7x + 10 sin(x). If f(0) f(x)? 3 and…

A:

Q: Calculate the higher derivative. (Use symbolic notation and fractions where needed.) d? 8 cos (1) =…

A: To find,  d2 dt28 cos2(t)

Q: 4) u = x² sin=1 x 5) Ø = tan¬1 3 0 6) y = In(7 – 3x)

A: This question is taken from the derivative in which we have to find the derivatives of the given…

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Q: The derivative of In (cos x) is A -tan x B None of the given choices tan x D sec x -sec x

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Q: Sketch, on separate graphs, each of the functions : (i)sinh(x). (ii)cosh(x). (iii)tanh(x).

A: Hyperbolic functions: These functions are defined as the algebraic expressions of the exponential…

Q: Express the given quantity in terms of sin x or cos x. sin (6t – x) O A. cosx- sin x O B. - sinx C.…

A: The given expression sin6π-x

Q: a. Use the definition of the derivative and the identity sin(a + B) = sin(a) cos(B) + cos(a) sin(B)…

A: As per Bartleby guidelines, for more than one questions asked, only one is to be answered. Please…

Q: At which of these x-values is the value of y=cos x greater than the value of y=sin x? Select all…

A: From above we can see that when x=π6, (cos x,sin x)=32,12 here cos x&gt; sin x From above we can see…

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

A:

Q: If f (x) = - sin(x), then f (11) (x) is equal to A - sin(x) B - cos(x) sin(x) D cos(x)

A: Differentiate 11 times

Q: Prove the identity. cosh(x) + sinh(x) - e

A: To prove the given identity we uses basic expression for sinh(x) and cosh(x).

Q: Given a tasked to solve for (x) = tan e Vx , Allan said she would apply the derivative of the ev…

A: Given f(x)=tan ex and after applying derivative allan got  f'(x)=exsec2ex2x we need to check wether…

Q: Consider the function on the interval (0, 2x). (x) = 4 sin? x + 4 sin x

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Q: Find the second derivative of f (z) = 6 sin (4z). %3D Enclose arguments of functions in parentheses.…

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Q: Consider the function f(x) whose second derivative is f''(x) = 9x + 8 sin(x). If f(0) = 2 and f'(0)…

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Q: a) If n is a positive integer, prove as given in image (b) Find a formula for the derivative of y…

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Q: Find the derivatives of the following 1. [sin-(2z – 1)]² 2. cos-1(sin z – cos z)

A: Differentiating complex functions is similar to differentiating the functions with respect to x, but…

Q: If f (x) = - cos(x), then f (0)(x) is equal to A - sin(x) B - cos(x) В © sin(x) D cos(x)

A: We have to differentiate the given function 9 times

Q: sinx In (2) cos:

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Q: Determine the extreme values of the function f(x) = 2 cos(x) –1 on the interval [0, 27].

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Q: Evaluate f sin° (x) cos“ (x)dx Select one: cos (x) cos" (x) + C 5 7

A: The given integral is ∫sin3xcos4x dx

Q: Find this second derivative: dz O 2 cos a? – 4x² - sin x² O 4x² cos x² – 2 sin æ² O 82² (cos z²)…

A: Given : Second derivate of sinx2

Q: If f (x) = - sin(x), then f (10) (x) is equal to = - sin(x), thenf (10) (x) is equal to A - sin(x) B…

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Q: Express the exact value of the function as a single fraction. Do not use a calculator.

A: Given: fθ=2 cosθ-cos 2θ To determine: fπ6

Q: 1. Evaluate the following: 3 sin z la. Give the equation of the tangent line to the graph of at the…

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Q: For what values of x in [0, 27] does the graph of f(x) = x + 2 sin x have a horizontal tangent line?…

A: The tangent line will be horizontal when the slope of the tangent line is zero. So if f'(c) = 0 at x…