Find the inverse of the following function and state its domain. f(x) = 4 sin(2x) Type 'arcsin' for the inverse sine function in your answer. f1 (x) = Domain= [

Q: Which of the following functions grow faster than ex as x→ ∞?Which grow at the same rate as ex?…

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Q: Use the chain rule to find the derivative of: cos (82® – 32) -

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Q: Find the derivative of the inverse of the following function at the specified point on the graph of…

A: Consider the given function  fx=sinx

Q: Find the derivative of the trigonometric function.

A: we need to find the derivative of the trigonometric function.  h(x)=sec6x

Q: Find the derivative of the trigonometric function.

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Q: Q2) By using the addition formula derive the identity of the function sin (x -)

A: We know that: sinA+B=sinAcosB+cosAsinB Replacing A by x and B by -π2:…

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: if x+1/x=2,find sin-1x

A: Given,

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A: To find the second derivative, the first derivative is to be found first. Now, since the function is…

Q: Give an equation of the resulting function when y = sin0 is horizontally stretched by a factor of 3.

A: To stretch or shrink the graph in the x direction, divide or multiply the input by a constant. for…

Q: Graph the function ƒ(x) = sin 2x + cos 3x.

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Q: cosx f(x) = 1+sinx

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Q: Q2) By using the addition formula derive the identity of the function sin (x-)

A: We have simply

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A: Graph the function:     Y=sin-12x-π2

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

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Q: (В) f (x) 3 3 sin(2x) — 4

A: we have to draw the curve of the function fx=3sin2x-4 let y=f(x). therefore, y=fxy=3sin2x-4 the…

Q: Use the first principles to find the derivative of cos(x -4x).

A: By the first principle  f'(x)=limh→0f(x+h)-f(x)h. So, dcosx2-4xdx=limh→0cosx+h2-4x+h-cosx2-4xh…

Q: By using the relationship between the hyperbolic sine function and its Ssinh- (x)] = V. inverse,…

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Q: culate the derivative of: (8x) COS f(x) = sin-(8a)

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Q: Derive the following function 7.y=sin(tan sin2x)

A: As per bartleby guidelines we only give first question answers.

Q: Determine the derivative of the following inverse trigonometric functions. 1. y = xsin x- +V1-x² 2.…

A: As we know that; The Power law; ddxxn=nxn-1 The product rule; f·g'=f'·g+f·g' The chain rule:…

Q: Find y" by implicit differentiation sin y + cos x = 1

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Q: 2. Arcsin(x/y) = 4x + 3y

A: Given: sin-1xy=4x+3y We know that ddxsin-1x=11-x2…

Q: What is the derivative of cos2t

A: Formulas used

Q: y = e*In(sinh x)

A: See the details solution in below

Q: Find the derivatives of Inverse trigonometric у - arccos V1 —х

A: y= cos-1(1-x)

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: 4x3 ソ= cos sin e2x

A: We have to simplify the derivative

Q: is x12 an even or odd function? Is sin x2 an even or odd function?

A: Note that -x12=x12. Thus, x12 is an even function.

Q: 6. When defining the inverse sine function, the domain of y = sin x is restricted to -÷<xs. a. Why…

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Q: у 3 3x? sin "(2x)+ 2х

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Q: What is the range of the inverse sine function y= sin- (x)? (-골, 글) A 2 2 B ( 0, π) 2'2 D [0, 1]

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Q: Differentiate the following functions: 5. y = sin-(n(2x + 1))

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Q: 106)Find the nth derivative of cosx cos2x cos3x AND ALSO FIND S dx sin?x

A: Cos2x = 2cos^2x -1

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A: Given:

Q: 7e e*²-sin(2x) sin(3x)sin(4x)

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Q: Write f(x) = -2 sin(x) + 4 cos(x) using a single sine function.

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Q: Differentiate the inverse trig function  y=Sin-1(Cos x/1+Sin x)

A: We use the chain rule and the quotient rule to find the derivative.…

Q: Find the derivative of the trigonometric function. h(x) = sec 6x

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Q: sinx In (2) cos:

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Q: ) In(sin(3x +2))

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Q: Arcsin(x/y) = 4x + 3y

A: We need to find the second derivative of the expression, sin-1xy=4x+3y...(1)

Q: 5. y = tan(x- +1

A: dtan-1(x)dx = 11+x2 dxndx = n.xn-1 dax+bdx = a2ax+b

Q: find the implicit formula of sinxy=x+y

A: Given,

Q: 1. Use the following methods to solve for the root of the equation f(x) = xe * – sinx

A: Let f(x)=xe-x-sin2x Given initial approximation is x1=0.5 then…

Q: Evaluate THT Sin 2X

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Q: Arcsin(x/y) = 4x + 3y

A: