The derivative of y = 3 cos (V1-x²) + (1-x²) ² can be written as 3 1– x² sin ( V1-x²) - (1-x² ) 7 3x y -. Determine the value of f(x) for X=0.43. (Use f(x) three(3) decimal place. Calculator must be in radian mode)

Q: Q2/ A/ Show that the functions f(x) = sin-1() and g(x) = 2tan-Vx, have the same derivative. %3D

A: Given : f(x)= sin-1 ( x-1 / x+1 ) g(x) = 2 tan-1 (√x)

Q: Find derivative of the following functions 1. y= sin^-1 2x^2 2. y= tan^-1 2x^2/5

A: Given 1. y=sin-1(2x2)2. y=tan-1(2x25)

Q: When f(0)=0 and f(pi)=0, what is the derivative of the function  7e^x + 6sin(x), and what is the…

A: Let the given function be:Applying the derivative with respect to x:Derivative of ex is ex and the…

Q: Find the derivative of the function.

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Q: Find the derivative of f(x)=sin sin(5x

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Q: Consider the function f (x) = sin β x,where β is a constant.   Verify that the function and its…

A: A function of the form p(q(x)) has its derivative by chain rule equal to p'(q(x))q'(x). For the…

Q: Find the slope of the graph of the function at the given point.

A: We have the given function as fx=4x5+3x-sinx          ⋯⋯1 As we know that, slope of a function fx is…

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: Which is the derivative of y= sin (x2-2x + 1)? (2х -2) (2x-2)Cos(x²-2x + 1)

A: We have to find derivative

Q: Consider the function f(x) whose second derivative is ƒ''(x) = 9x + 6 sin(x). If ƒ(0) = 4 and f'(0)…

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Q: 4. Find the derivative of the following function. 1+ sin x 8(x) = 1+ cos x

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Q: Consider the function f(x) whose second derivative is f''(x) = 4x + 6 sin(x). If f(0) = 3 and f'(0)…

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Q: What is the derivative of y = sin(3x²) cos(3x²)

A: We have to find the derivative of given function.

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: Find the derivative of cos-¹(sin x)

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Q: What is the derivative of tan-1(e2x-1), 2e 2r -1 2e 2x -1 2e 2r -1 (D) 1+ er-2

A: Solution : We have to find out the derivative of the give function tan-1e2x-1

Q: 12. The derivative of cos(1 – x) with respect to x is ;A. - sin(1 – x) B sin(1 – x) C -(1– x) sin(1–…

A: Given that: Let f(x)=cos(1-x)

Q: h(x) = V1+ sin(3x²) %3D

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Q: Find the derivative of y with respect to x. y = 5x4 sin-1 r 1 V1-x? + 20x3 5x4 1+x2 + 20x³ sin¬1 x…

A: We have to find the derivative.

Q: The third derivative of y = sin is 1 -sin b) y" = --cos 1 а) у 8. 2 2 c) y" =-8sin d) y" = -8 cos

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Q: Find the second derivative of f(x) = 9 sin (2x). Enclose arguments of functions in parentheses. For…

A: On solving this we will get

Q: Find the first derivative of y = cos4 x – sin4 x and y = x3   –  x2 cos x  +  2x sin x  + 2 cos x…

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Q: find the derivative of f(x) = cos(sin(4x+7)^4). simplify

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Q: (a) Find the derivative of the function g(x) = sin2 x + cos2 x (b) then use a trigonometric…

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Q: Find the derivative of f(θ)=(sinθ/1+cosθ)^2

A: differentiate wrt theta

Q: Find a formula for y" (the second derivative) if y = 2* · sin x.

A: Given that, y=2xsinx            ...(1)

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

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Q: В. f(x) = (sin ebx³ ). 3 |cot(26x) x4 -

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Q: Solve for the derivative of the following trigonometric functions. 1. f(x) = e3x 2. f(x) = x³ ex 3.…

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Q: Find the second derivative of the function. f(x) = sin(2x?) %3D f "(x) = 16x sin 2x) + 4 cos 22)

A: Given f(x)=sin(2x2) Formula: Derivative of sinx  = cosx Derivative of cosx = -sinx

Q: r (4x2 – 3x + 5)* - 3.) c(x) = %3D sin x

A: solution:- find the derivative by using the quotient rule

Q: Find the slope of the graph of the function at the given point.                         f(x) = 4x5 +…

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Q: g(x)%3Dx sin(2*)

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Q: f(x) = 2 cos I - 3:

A: Of a function y = f(x) of a variable x is a measure of the rate at which the value y of the function…

Q: Find the derivative of the function. Simplify where possible. y   = Cos-1(Sin-1t)

A: y=cos-1sin-1t

Q: b) Use implicit differentiation to find for the equation yz? -e** cos (4zx)–3y² =4. F. DO NOT use…

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Q: Which is the derivative of y= sin (x2-2x + 1)? О 2х-2) (2x-2)Cos(x²-2x + 1) O Option 2

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Q: Q1/ Choose the appropriate function for this derivative sin x cos x V1+ cosx 2/1+ cos x

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Q: Find the derivatives of the functions y = 3/(5x2 + sin 2x)3/2

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Q: Consider the function f(x) whose second derivative is f''(x) = 10x + 8 sin(x). If f(0) = 3 and f'(0)…

A: Given, f''(x)=10x+8sinx(x) After integrating the above equation,…

Q: Find the derivative of y with respect to x for y = (- 7x2 – 5x + 5) (sin x + 11x) 1x + ..... The…

A: Given:- y = (-7x2-5x+5) (sin(x) +11x)  To find:- Derivative of y

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: 1+sin 2x 1) Find the derivative of f(x) = 2 cos x

A: To find The derivative of given f(x)

Q: Solve for the derivative of the Trigonometric Differentiation. 1. y = sin (5x) + 3x cos (5x) 2. y…

A: given y=sin5x+3cos5xdiffrentiate w.r.t. xdydx=ddxsin5x+3cos5xdydx=ddx(sin5x)+ddx(3cos5x)we know that…

Q: Find the third derivative [f"(x)] of the given function: f(x) = 8 sin() %3D

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

A: We have to find out derivative

Q: Consider the function f(x) whose second derivative is f''(x) = 9x + 10 sin(x). If f(0) = 3 and f'(0)…

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Q: How are the derivatives of sin-1 x and cos-1 x related?

A: Given functions are sin-1x and cos-1x

Q: What is the derivative of the function h(x) = ((4x^2-4)/(cos(x)))^8

A: We have to find the derivative of ((4x^2-4)/(cos(x)))^8 = 4^8(x^2-1) sec^8(x)= 65536(x^2-1)sec^8(x)