Consider the function below. z = sin(x) - sin(y)

Q: Find the first and second derivatives of the function. g(t) = 2 cos t - 3sin t

A: We find the first derivative

Q: xpress tiIE SS the f (x) = 3 sin? x + cos? x of oog m

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Q: mby f(x) = (lnx) (sin x). The figure above

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Q: Differentiate the function. f(x) = sin(3 In(x)) f'(x) = %3D Need Help? Read It Wa

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Q: Evaluate sin(x+y)-cos(x+y)=1

A: Given: sinx+y-cosx+y=1 Dividing both sides by 2, we get  12sinx+y-12cosx+y=12

Q: 43. What are the periods of these functions? (a) y = sin 20 (c) y = sin 20 + sin (b) y = sin

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Q: sin' xcos* x dx x cos

A: Perform integration

Q: B. Derivatives of Trigonometric Functions dy Using the formula find dx 5. у-сos (2x-1)

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Q: 3 - What is the domain of the function f(x) ? sin x + cos X

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Q: F f(z) = -3e sinr, the second derivative f"(x) is: %3D

A: Given f(x)=-3ex·sinx Taking first derivative with respect to x, we get f'(x)=-3ddx(ex·sinx)…

Q: 1. Differentiate the function: y = arccos(sin x)

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Q: у 3 sin (x? + 3x + 1) 1. 2. у%3D сos?(2х — 1) y = tan vx2 – 1 3.

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Q: B. Derivatives of Trigonometric Functions Using the formula find- dy dx 7. y= sin In(4x + 3)

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Q: 7 sin x Let f(x) 6 sin x + 2 cos x Then f'(x) = The equation of the tangent line to y = f(x) at a =…

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Q: f (x) = 3 sin x + 3 cos x, [0, 27]

A: Consider the function: fx=3sinx+3cosx Differentiate the given function with respect to “x” then,…

Q: sin x+3 cosr dx. Determine the following rational function 1+cosx

A: We have to first do partial fraction of the given expression.

Q: 1. Find f* dx by hand and show how to check the result is correct by differentiation.

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Q: Rewrite the expression as an algebraic function of x and y. sin(cos-1(x) – tan-1(y))

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Q: 6 sin æ Let f(x) %3D 6 sin x + 4 cos æ Then f'(x) = The equation of the tangent line to y = f(x) at…

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Q: ind by implicit differentiation if y is defined as a function of x by the equation xy' + x? = x + 3y

A: Topic = Differentiation

Q: Find local and extreme values of f(x) = x + sin x, [0, 1].

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Q: 33. For what values of x does the graph of f(x) = x +2 sin x have a horizontal tangent? %3D

A: We need to find values for which the function have horizontal tangent.

Q: y = sin(In 2x) a. sinx b. In 2x c. cos(ln 2x) cos(In 2x) d.

A: From the chain rule of differentiation, ddxu(v(x))=dudv×dvdx Here, v=ln(2x) and u= sin(v),

Q: 3 Determine the amplitude of the function y =- cos(x). Also, choose its graph. The amplitude is

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Q: 1. Differentiate the function: Y = arccos(sin x)

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Q: The function f(z) = e-y sinx is harmonic function True O False O O

A: A function f is said to be harmonic function if it is satisfied Laplace equation

Q: snip

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Q: III. Find y' using implicit differentiation given the following functions

A: Please refer to the image below

Q: a . Show that y = sin x, y = cos x, and y = a cos x + b sin x (a and b constants) all satisfy the…

A: a. Given

Q: 11. y x Sin x + (1 -x) Cos x Oa. x Sin x+ 2x Cos x b.x² Sin x ©* Sin x dxSin x+ 2 Sin x

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Q: Write the equation of the normal line (a line perpendicular to the tangent line) to f(x)=2−cosx at…

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Q: Find a0 of the function f(x) = sin(x/2

A: Given function is:  fx=sinx2

Q: f(r) = 5 sin(sin(x)) %3D

A: answer is in next step

Q: The range of the trigonometric function f (x) = 1 + tanx is a) (-0, +0) b) (-1,1) c) [0,2] d) [-1,1]

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Q: d 10.(4* tan x) dx

A: Find the derivative

Q: d cos a In(x + a) dx da sina

A: Given ddα∫sinαcosαlnx+αdx

Q: -1 If f (x) = sin(x), then what is the value of f' () in simplest form? %3D

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Q: sin x At what points is the function y = continuous? 4x

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Q: domain of g(t)= sin(et-1)

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Q: Find the domain of the function y = tan(x/2)

A: As we know that the domain of the function y=tan(x) is all real numbers except the values where…

Q: a. f (x) = sin x %3D

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

Q: Consider the following function. Vx, (1, 1) (a) Find an equation of the tangent line to the graph of…

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Q: The range of the trigonometric function f(x) = sin (x- is %3D a) (-00, +0) b) [-1,1] c) [0,2] d)…

A: The given function is f(x)=sinx-π2

Q: Diffcrentiate the function sin x 2 tan x

A: Please refer the attached image for complete solution.

Q: 7 sin x Let f(x) 2 sin x + 6 cos x Then f'(x) The equation of the tangent line to y = f(x) at a =…

A: Given problem:- f(x) =7 sin(x)/(2 sin(x) +6 cos(x))  Find:- f'(x) and equation of tangent line at…

Q: 2. Use Implicit Differentiation answer the following: (a) Find y' given y° + xy = x´+ x - y

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Q: • sin ( x ) + t)dt cos(t*) h(x) = -3 h'(x) = Preview Enter an algebraic expression [more..]

A: Given,

Q: Textbook Videos [+] Consider the function f(x) whose second derivative is f''(x) = 9x + 8 sin(x). If…

A: Proceed as shown below

Q: What is the type of function for f(x)=x'+sin(5x). O Even function Odd function Neither function

A: The given function is  f(x)=x3+sin(5x) ....(1) And are asking to check whether f(x) is even , odd…