Which of the following functions does not have the property that f(x) =f(4)(x) ? A f(x) = sinx B f(x) = cosx (c) f(x)= e²x D f(x) = e-x

Q: Find the first derivative of g(x) = - 5 In(x)cos(r"). g'(x) =

A:

Q: Given g(x) = ln[(x^1/3 + sinx - 3tanx)/3x^4 - x^1/2], calculate g'(x)

A: Given equation is , gx=lnx13+sinx-3tanx3x4-x12 Let's find g'(x) Formulae we are using here,…

Q: Find the derivative of 2 cos x 1. f(x) x+1

A: As we know that: The Power rule: ddxxn=nxn-1 The Quotient rule: fg'=f'·g-g'·fg2 Given: fx=2cosxx+1

Q: Find the second derivative of the following  a .) 2x^3- 1/2x b.) Cos(x^2)

A: The given functions are  a) 2x3 - 1/(2x) b) cos(x2)

Q: compute the derivative y = sin(2x) cos2 x

A: Given y=sin(2x)cos2x The product rule of derivative is given by:

Q: Consider the function f(x) whose second derivative is f"(x) = 3x + 8 sin(x). If f(0) = 2 and f'(0)…

A: Consider the second derivative function, f''x=3x+8sinx Given, f0=2  and f'0=2 We need to find f(x).…

Q: The derivative of f(x) = 5x – Vx + (sin)x – e² -

A: Given; f(x)=5x4-x1/3+[sin(π/2)]x-e2

Q: f(x) = ln(cos3(2x+1)5)     f'(x) = ?

A: Given that f(x) = ln(cos3(2x+1)5)

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

A: Given,

Q: If f(x) = sinh³ x %3D the en f'(x) = ||

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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)…

A:

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

A: We have to find f(x) and find f(3) using given intial condition

Q: The derivative of the function f is defined by f'(x) = x² – x – 2 cos (x2). If f(3) = 2, then use a…

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Q: f(x) = e2 sin¯+(3x) + In (cosh-1(e³x))

A:

Q: 1 Find the derivative of g(x)= (x)sec(x) + a+ x* + cos - sin(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=cos3(5x)

A: To find the derivative of: y=cos3(5x) For that use chain rule and ddx(xn)=nxn-1ddx(cos x)=-sin x

Q: Consider the function f(x) whose second derivative is f''(x) = 3x + 8 sin(x). If f(0) = 4 and f'(0)…

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Q: (a) From sin2 x + cos2 x = 1, we have f(x) + g(x) = 1. Take the derivative of both sides of this…

A: (a) From sin2 x + cos2 x = 1, we have f(x) + g(x) = 1. Take the derivative of both sides of this…

Q: Consider the function f(x) whose second derivative is f''(x) 8x + 3 sin(x). If f(0) = 4 and f'(0) =…

A: Given : f"(x) = 8x + 3 sinx, f(0) = 4, f'(0) = 4,    To find : f(5)?

Q: 7. The derivatives of the function f (x) = cos(3x²) that follow are incorrect. What misconception…

A: The differentiation of product two functions can be calculated by using the formula,…

Q: compute the derivative. y = sin(2x) cos2 x

A: We can find the derivative of this function by using the product rule of differentiation . According…

Q: Find the extreme values of the function f(x) = sin(2x) within the interval 0 < x < 2n %3D

A: Given function f(x)= sin(2x)            0≤x≤2π

Q: If f(x) = COS X then f' (x) equals: X S0)- -sin x cos X:

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Q: Find the derivative f'(x): f(x)= cos-1x / x+1

A: To find the derivative of the given function.

Q: Find the anti-derivative of the following: a.) f(x)=4x1/2-(4/x1/2) b.)…

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: 3. Evaluate f x sin2 (x²) dx.

A: Given I=∫x sin2x2 dx To Find I

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

A:

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

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Q: g(x) = cos ¹x+ 1-x

A:

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

A: see the details solution in below

Q: Consider the function f(x) whose second derivative is f"(x) = 9x + 6 sin(x). If f(0) = 2 and f'(0) =…

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Q: If f (x) = - cos(x), then f (10) (x) is equal to (A) - sin (x) ® -cos(x) © sin(x) D cos(x)

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Q: (a) Find the derivative of cos(1+x²).

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Q: (A) Find the first derivative of the following function: 1+ cos2x f(x) = %3D 1- cos2x |

A:

Q: Consider the function f(x) whose second derivative is f''(x) = 7x + 3 sin(x). If f(0) = 3 and f'(0)…

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Q: Find the function f(x) whose derivatives is sin x and whose graph passes through the point (0,2). O…

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Q: Find the derivative and simplify A. f(x) = 2 sin−1(4x + 5) B. f(x) = x3tan−1(x2)

A: Given:- A.   f(x) = 2 sin-1 (4x + 5)   B.    f(x) = x3 tan-1 (x2)  To find :- Derivative of given…

Q: Find the first and second derivatives of the function. f (x) = In(cos x)

A: We will use the chain rule and quotient rule of differentiation to find the first derivative and the…

Q: Use the chain rule to find the derivative of: cos(7 + 8x)

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

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Q: 2) Find the derivative of the following func (c). f(x) = (x+ 7 sin z) (1 – 5 cos x) tanx (d). g(x) =…

A: We can find the answers as below.

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

A: Given function is f"(x) = 9x + 10sin(x)

Q: Differentiate implicitly for the equation for x^2y+x^3-cos(x)=3y^2

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

A: We have to find out derivative

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)