The function f(x) =x° +6 is one-to-one. Find an equation forfx), the inverse function. f'x) =O (Type an expression for the inverse. Use integers or fractions for any numbers in the expression.)

Q: If f(x)=2 sin x/1+cos x, then f′(x) =    f′(4) =

A: We have to find

Q: If f(x) = 4x(sin x + cos a), find f'(x) = COS f'(2) =

A:

Q: Differentiate the function.

A: We write the expression using an exponent first

Q: If f(x) = 3e cos(x), find f '(x) and f "(x).

A: Given,          fx=3excosx

Q: If f(x) = f'(x) = 1 COS :−¹(5x²), find f'(x). Use exact values.

A:

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: If f(x) = 2 sin-1 (xª), then f'(x) =

A:

Q: Given the equation 3 sin 2xy = 1, evaluate . Assume that the equation implicitly defines y as a…

A: Given equation: 3sin2xy=1

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

A: We have simply

Q: Express cos°x as a function of multiple angles.

A: The function of multiple angles is given below,

Q: If f(x) = 5x(sin x + cos x), what is f'(x)?

A:

Q: for - 1<x<1. Prove that for the inverse cosine function, (cos- x) = dx 1-x

A: Here, the objective is to prove the following:  ddxcos-1x=-11-x2   -1&lt;x&lt;1

Q: 1. y = sin(4x) 2. y = sin(4(x - )

A: We need to find period of given function.

Q: If f(x) = (52² + lx + 6)cos(x), find f'(x) =

A:

Q: 1 y = cos (2*)

A:

Q: Find if f(x, y) = x2 +2xy cos x .

A:

Q: Find f if f''(x)=2+cos(x), f(0)=−2, f(pi/2)=6 f(x)= ?

A: Please see the white board. C1 is the constant of integration.

Q: Using appropriate substitution, f sin°(x)cos³ (x)dx is equal to:

A:

Q: Which of these will represent u in the function * y= sin -1 Vx2 + 3x + 4? Sin-1 а. du V1-u?

A: Using definition of composite function.

Q: If f(x) = 7 sin(8a)sin-(x), f'(x) -

A:

Q: If f(x) = 4x sin x cos x, find f'(x)= %3D

A:

Q: Find a function F(x) satisfying F'(x) = sin(6x).

A: Solution  Let consider differential  F'(x)  of function F(x)  so F(x)=∫F'(x)…

Q: Is the function f(x)=sin(3x)+cos(tan x) even, odd, or neither? Why?

A: Recall: A function f(x) is even if  f(x) =f(-x). A function f(x) is odd if f(x)=-f(-x)

Q: 2. Differentiate each function with respect to x: (a) y = cos (3x²) (b) y = sin (1 + 3x)

A: Our Aim is to differentiate the given functions with respect to x:-(a) y=cos (3x2)(b) y= sin (1+3x)

Q: find the derivative d/du 1/(1+cos2(u))1/2

A: given:    ddu(11+cos2u)

Q: If f(x) = f (x) „sin(x) e Then f'(0) = ?

A:

Q: Determine whether the statement makes sense or does not make sense, and explain your reasoning.

A: Domain of function sinx is -π2,π2. Therefore, y=sinx has inverse function if x is restricted to…

Q: 1. f(x) = cos (-:-)

A: From graph, it is clearlimx→∞cos1x =limx→-∞cos1x = 1

Q: Calculate f/2 ( sin a) da xp

A:

Q: If f(x) = 2x(sina + cos a), find f'(x) = %3D

A:

Q: у 3 3x? sin "(2x)+ 2х

A:

Q: If f(x)= cos(4x) Plot the function from (x=0) to (x=180)

A:

Q: What is the relationship between the domain of a the function y = sin x and the range of the…

A: Topic:- range and domain of trigonometry function

Q: 4 If f(x) = sin* a, find f'(x). %3D Find f'(2).

A:

Q: If f(x) = [sin(x)]², what is f'(x)?

A:

Q: If f(x) = 3x(sin x + cos a), find f'(æ) =

A:

Q: If f(x) = 4x(sin a + cos x), find f'(x) = f'(5) =

A:

Q: If f(x) = e2" [sin(=)]°, what is f'(x)?

A:

Q: Use trigonometric substitutions to find dx. V1-

A:

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: What is the range of the function y = sin-1x? Select one: 2' 2 (-플, 끌) 2' 2 O [-1, 1] O [0, 1] 프2 프2

A: Given function is y=sin-1x

Q: If f (x) = e2*[sin(x)]², what is f' (x)?

A:

Q: Given f(x) = cos(2), find f' (x) in simplest form.

A: According o question given fx=cos-1x2We have to calculate the f'(x)

Q: Find f, f '''(x) = cos(x),    f(0) = 8,    f '(0) = 5,    f ''(0) = 4

A:

Q: If f(x) = cos(ln(x5)), find f ′(1).

A: Given that          f(x) = cos(ln(x5)) Here we have to find f'(1).

Q: Determine whether each function is even or odd  (d) y = cos x   is an ______ function (e) y = 2…

A: Determine whether each function is even or odd  (d) y = cos x is an ______ function (e) y = 2 cos x…

Q: If f(x) = cos(sin(x°)), then f'(x)

A: The givne function is f(x)=cossinx6 We have to find f'(x)=?

Q: Find the function f(x) if f'(x) = 2 cos x + 3 sin x and f(0) = 4

A: We have