Let f(x) - 6 cos 6 cos° x f '(x) =

Q: Find the first derivative of g(x) = - 5 In(x)cos(r"). g'(x) =

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Q: Find the critical points of the function f(x)=sin2x−cosx on the interval (0,2π).

A: For critical points, first find the derivative of the function and equate it to zero.

Q: Integrate sin^2(7x)-cos(x)

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Q: if f(x)=ln(1+cosx) then find f`(x)

A: f'(x)=(1+cos(x))'/(1+cos(x))      =-sin(x)/(1+cos(x))

Q: What is the critical point of the function f (x) = cos x?

A: what is the critical point of f(x)=cos(x)? for critical point, f'(x)=0

Q: Find the first derivative of  y = (x – 1) √ (2x – x2)   + arcsin (x – 1), and y = arctan [ (3 sin x)…

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Q: Determine of y = cos(x) – V5a2 In x.

A: I have stated the used formulas in the solution.

Q: |2tan x In (cos x) dx=

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Q: Solve using implicit differentiation.    y cos x = x2 - y2

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Q: 2tan x In (cos x) dx=

A: here we have to integrate the given integral.

Q: Consider the function f(x) whose second derivative is f′′(x) = 18x + 3 cos x. If f(0) = 4 and f′(0)…

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

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

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Q: Find the second derivative of f(x) = x2+ e* - COSX. O a. f(x) = 2x + xex - cosx O b. f'(x) = 2x + e*…

A: Solve by derivative

Q: 9.) JE sin°(x)cos*(x)dx 11.) F sin°(x)cos²(x)dx 2

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the extreme values for f(x) = sin(x) + cos(x) on the interval [0, 2π].

A: The given function is f(x)=sinx+cosx   and the interval is 0, 2π. We have to find extrema on the…

Q: Differentiate y = coS 7 + sin4x+ x cos x + 4 with respect to x. 1. 2.

A: the given function is: y=cosπ+sin-1(4x)+xcos(x)+4x3 we have to differentiate the given function with…

Q: Compute integral sin(cos(x^2)) sin(x^2)x dx

A: Explanation is given below...

Q: Evaluate: S Arctan 2 sin²x dx . Arctan 1 cos+x

A: Given,  ∫Arctan1Arctan2sin2xcos4xdx

Q: If f(x) = COS X then f' (x) equals: X S0)- -sin x cos X:

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Q: The derivatives of sin- 1 x and cos- 1 x are negatives of each other.

A: From the question it's not clear, what do you want us to do with it. I assume that you want to know…

Q: Find the second order derivatives of the function f(x) ex sinx cos 2x

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Q: What is the derivative of f(x) =2cos (x)? %3D 2 cos (2x) O -2 cos (2x) O 2 sin (2x) -2 sin (2x)

A: f(x) =2cos2xdifferentiating w.r.t xd(f(x))dx=ddx(2cos2x)

Q: find integral sin 5 x  cos 2  x dx

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Q: Find the smallest positive zero of f(x)=cos^2(x)-sin^2(x)

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Q: Find constants c1 and c2 such that F (x) = c1 sin 3x + c2x cos 3x is anantiderivative of f(x) = 2x…

A: Given: Fx=C1sin3x+C2cos3x and the antiderivative of F(x) is fx=2x sin3x To find the constants C1 and…

Q: 2. Integrate using Trig: cos° x dx

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Q: Find and locate the local and absolute extreme values of f(x) = x+(sin2x) in [0, π].

A: Find and locate the local and absolute extreme values of f(x) = x+(sin2x)in [0, π].

Q: Differentiate y = coS 7 + sin4x+ x cos x + 4 with respect to x. 1.

A: 1) The given equation is y=cosπ+sin-14x+xcosx+4x3 To find: dydx

Q: If f (x) = - cos(x), then f (10) (x) is equal to (A) - sin (x) ® -cos(x) © sin(x) D cos(x)

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Q: f(x) = cos (In (3x))

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Q: Compute the derivative f'(x)given sin x 1 dt 1- 12 f(x) = cos x

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Q: (A) Find the first derivative of the following function: 1+ cos2x f(x) = %3D 1- cos2x |

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Q: Estimate cos(x²)dx by using a right-hand sum and 4 subintervals. |cos(x²)

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Q: Find if dy dx y = (cos x) * O (cos x) * (-sin x) O (sin x) * (In cos x - x tan x) O (sin x)* (In cos…

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Q: Differentiate the function. f(x) = sin(x) In(3x) sin (x) f '(x) + cos (x) In (3x)

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Q: The value of function f(x) = sin x (1 + cos x) is maximum when x is equal to

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Q: Find the first and second derivatives of the function. f (x) = In(cos x)

A: We will use the chain rule and quotient rule of differentiation to find the first derivative and the…

Q: sinx f(x) = on [0, 2n] cos x-V2

A: Given :         f(x) = sin xcos x - 2 on 0, 2π   To determine the extrema of the above function…

Q: Evaluate sin (4x) cos -2(4x) dx. | sin (4x) cos -2(4x) dx = O

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Q: Find the derivative of both a and b a. x csc-1(1/x) b.(esin2x)/[In(cos2x)]2

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Q: Find the first derivative: In 2x f (x) 1- In 2x f(x) = In (sec x) f(x) = cos (In x) f(x) = In[cos…

A: we can answer only three subparts, or the first question and the rest can be reposted. No more than…

Q: Compute the derivative d tan x dx \cos x – 4)

A: To compute :

Q: x sin 2x sin cos x 2 X. Prove that 8 dx 2х - л

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Q: Differentiate implicitly for the equation for x^2y+x^3-cos(x)=3y^2

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Q: Find the derivative of a. (e(sin2x))/[In(cos2x)]2

A: We have to find out derivative

Q: Compute the derivative d tan x dx \cos x – 4

A: Given: Formula Used:

Q: Compute f sin(cos(x²)) sin(x²)x dx

A: