Is the function h(x) = 3 cos x+ sin x concave up or down at the point 3 я?

Q: If f(z) = 3x(sinx + cos x), find f'(x). f'(x) = 3z cos( z) 3z sin(z) + 3 sin(z) + 3 cos( z) Evaluate…

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Q: y=8sin(x)cos(x) ; x=pi/3

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Q: For which values of x are y = sinh x and y = cosh x increasing anddecreasing?

A: Hence, sinh x is increasing for all x.

Q: Find all critical points of the function: R(θ) = cos θ + sin2 θ

A: The derivative is defined as the rate of change of one quantity with respect to another. In order to…

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: 1) Find 4 by implicit differentiation given 4 cos x sin y = 1. dx

A: Differentiate above equation with respect to x.

Q: Q1/Prove that S cosh(2x)sinh(x)dx = cosh(3x) – cosh(x)) -

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Q: Find the derivative of f(2) = sinh(2²) – 2z cos(32). Is this an analytic functio %3D

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Q: Find the x values of all the horizontal tangents to the function f(x) = cos.x + /3 sinx on the…

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

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Q: Find the tangent line to the function f(x) = 2x cos4(x) at the point (0,1)

A: We have given function fx=2xcos4x and point 0,1. We have to find tangent line to the function at the…

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: ayfor gen f(x) = cos (2r + (/2)), a = /4 TT

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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: What value for a will make sinx { ,X # 0 2x f(x) = %3D 3D ,X = 0 a continuous function?

A: For a function f(x) to be continuous at x = a,limx→a-f(x) = limx→a+f(x) = f(a)

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

A: Given,  ∫Arctan1Arctan2sin2xcos4xdx

Q: Determine whether f(x) is differentiable at x = 0. Show your work. sin(x) cos(x)-1 3x + 1 f(x): = if…

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Q: Find the derivatives of the functions in Exercis

A: fθ=sinθ1+cosθ2

Q: Calculate the derivative. y = cos 3x In (cos ²3x) y' =D %3D

A: We can find the derivative as below.

Q: Show that bothy= sinx and y = cos x satisfy y" = -y

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

Q: Evaluate sin(x) · In ( cos(x)) dx using integration by parts.

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Q: Find the most general antiderivative of the function. f(x) = 5 cosx-7 sinx

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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: What is the derivative of 0.50 sin 2t+0.30 cos t

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Q: Find the second derivative of f (z) = 6 sin (5z). %3D Enclose arguments of functions in parentheses.…

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Q: Consider f(x) = 3 − cosx on the interval [0, 7]. When will the first derivative equal zero?

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Q: FInd the length of the curve y= 2ln ( sin(x/2)) from x = π/5 to x = π

A: Formula to find the length of the curve is  ∫ab1+dydx2dxGiven y=2ln(sinx2) Lets find out dy/dx by…

Q: Describe the method used to integrate sinm x cosn x, for m even and n odd.

A: Method to integrate sinmx cosnx ,for m even and n odd. Let m=2k and n=2k+1 ∫sinmxcosnx…

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: Find the equation of line tangent of sin(2x) cos(3x)+ sec(x) TC At x = 6. %3D

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Q: 9. For f(x) = arctan (2 sin ( Vx )) , compute the first derivative at the point %3D X =

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Q: Find all x values in interval [0,2 ·¤] on the graph of f(x) = -3·sin(x)·cos(x) where the tangent…

A: Given,            f(x) = -3 sin(x) cos(x)

Q: What is the second derivative of y + Incosx = 0 * O (cos x) ^2 O 1 O (sec x)^2 tan x

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Q: differentiate the function: y= ln(x^9 sin^2(x)) y'(x)=

A: Given function as

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

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Q: Find the linearization of ƒ(x) = sqrt(x + 1) + sin x at x = 0. How is it related to the individual…

A: To determine the linearization of the function at x=0.

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

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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: Find all extreme values for y=x+sinx^2 over [0,π]

A: Given,  y = x + sin2x  We have to find the extreme value in the interval 0, π

Q: Find the fourth derivative of f (z) = 3* + In (z) – 191z. Enclose arguments of functions in…

A: To find :  Fourth derivative of function ,  f(x)=3x+lnx-191x

Q: Find the derivative. 3t cos (t) dt %3D O 3x cos (x4) O &va cos (x4) O 3 cos (x4) - 3x sin (x4) O cos…

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Q: 1. Find the point(s) if any where f has a horizontal tangent line. у %3D УЗх + 2 cos x 0<x < 2п

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Q: Find all x values on the graph of f(x) = - 3 sin x cos x where the tangent line is horizontal.

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Q: b. Find the derivative of y = Scos (x) sin(3–2x) + tan2(3x² – 4x) – csc(V2x – 1 Jand express your…

A: To find the derivative of below equation

Q: 3. It is given that sin(x) + cos(x) tan(y) = 1. Use implicit differentiation to find

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

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Q: Given the function y = 6 cos(3x + 1) The second derivative y" %3D Select one: 18 sin (3x + 1) -18…

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Q: Find the most general antiderivative. Verify with differentiation f(x)=cosx + 2sec^2x

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Q: Differentiate with respect to the independent variable. f(x)= (e^x + cos x)^6 (3x^4 - sin x)^2

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