What is the value of f' () if f(x) tan x 1 1+ 2 Option 1 Option 2 1- 2 2 O Option 3 O Option 4 EIN 1,

Q: What are all absolute and relative extreme values of the function f(x)=– sin z on the interval (0,…

A: Given function f(x) - f(x) = -sinxDifferentiating on both sides with respect to x - f'(x) =…

Q: ) The tangent line to y = f(x) at (-5, 2) passes through the point (-7, -5). Compute the following.…

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Q: Consider the function f(x) whose second derivative is f”(x) = 10x + 8sin(x) If f(0) = 2 and f’(0) =…

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Q: 4. Is the function given by G(x) 1 x-1 the interval (0, ∞)? Why or why not? continuous over

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Q: Consider the function f(x) whose second derivative is f”(x)=5x+2sin(x). If f(0)=4 and f’(0)=4, what…

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Q: If 1– cosh x f(x) : 3+ cosh x then f'(x) =

A: The quotient rule of the differentiation uv'=u'⋅v−u⋅v'v2.

Q: Compute the derivative. f(x) = (cos2 x)cosx

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Q: How can we use the derivative f'(x) of a function f(x) to determine where the local max(s) and…

A: Given query is to provide the procedure to find local max and min with the use of derivative of a…

Q: 2) Find the derivative of f(x) = tan(1+ cos 3 x) %3D

A: As the function involved function in a function we can apply chain rule and find the derivative of…

Q: Find the relative extrema of f(x) = 8+ 126x – 7x2 using both first and second derivative tests. f…

A: If second derivative is less than zero then there is relative maxima.

Q: If f(x)= 8-cosh x/6+cosh x then f'(x)=

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Q: Find the hundredth derivative of the function f (x) = cos(2x). O f(100) (x) = -2!00 cos(2x) O f(100)…

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Q: If f(x)=tanh(3x)f(x)=tanh(3x) then f'(x)=f′(x)=

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Q: If f(x) = etan-¹(x²-3) then f'(x) at x = 2 is equal to

A: SOLUTION-

Q: 28. The derivative of In(x sin x) is 1. 1 + cotx а. b. C. d. tan x +x - +x sinx

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Q: 3. Is the function given by x²-4x-5 -,x< 5 f(x) =. x-5 x+1, x 2 5 continuous atx=5? Why or why not?

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Q: Find the second derivative of the function.

A: Given: fx=x cosx Now to find the derivative of the given function, Differentiate given function with…

Q: What is the derivative of x 3 sin(x)? Select one: (sin(x) + 3x cos(x)) 2 Зх 3 + cos(x) 2 Зх 3 2 O…

A: Derivative of the function

Q: The function f(x) = x^2 is decrea sin g on (- ∞,0)  True or False

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Q: Differentiate f (x) = (ex + e-x)/(ex - e-x)

A: We have to differentiate the function: fx=ex+e-xex-e-x Here two function are in ratio so we need to…

Q: Find the local maximum and minimum values of f using the Second Derivative Test. If the Second…

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Q: 1 F(x) = -1. tanh 3x

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Q: Apply the first derivative test to indentify all relative extrema. f(x) = cos² (2x)

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Q: If the derivative of f is f'(x) = (x – 1)(x + 2), then f is decreasing on (-2, 1) Select one: True…

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Q: The derivative of the function f (x) 3x tan x is Select one: O f'(x) = 3 tan x + 3x sec² x O f'(x) =…

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Q: The tangent line to y = f(x) at (-1,-8) passes through the point (-7,5). Compute the following a.)…

A: The tangent line to y=f(x) at (-1,-8) passes through the point (-7,5)

Q: Consider Mean Value theorem for derivative for function f(x) 4(1-2x) in interval [0,1]. TCOS(TX) -

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Q: What is the derivative of f(x)=−cos(x)+4sin(x) at the point x=−π/2?

A: We will find the derivative as following.

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

A: Consider the function f(x) It's second derivative is f''(x)=4x+3sin(x)If f(0)=3 and f'(0)=4   We…

Q: The second derivative of y = ln(sec x) is а) у 1 - tan x b) y = tanx sec x c) y = secx · tan x d) y"…

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Q: What is f(2022) (cos x), the 2022nd derivative of f(x) = cos x? COS X sin a sina

A: To find 2022nd derivative of f(x) = cos(x).

Q: Consider the function f(x) whose second derivative is f''(x)=8x+10sin(x). If f(0)=3 and f'(0)=2 what…

A: The function is f"x=8x+10sinx.   Integrate the function.…

Q: Let S(x) =x²- sin²(x). What is the correct result of the derivative of f with respect to x? A s'(x)…

A: To solve the given differentiation problem.

Q: Find the x-value of the extrema by using the Second Derivative Test. Justify your answer. f(x) =…

A: As per the question, we need to find out the x value of the extreme, for bubble 3 only. For (3),…

Q: Find the derivative of the algebraic functions f(x) = x (1-) x+3, : g(x) = x + cotx

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Q: Find the hundredth derivative of the function f (x) = cos(2x) . O f(100) (x) = -2100 cos(2x) O…

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Q: The derivative of the function f (x) = 3 sin“ x is Select one: O f'(x) = 12 cos³x O f'(x) = 12 sin³…

A: dsinxdx = cosx

Q: Find the derivative of f(x) = sec(tan(x) + cot(x))

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Q: What is the second derivative of y + Incosx = 0 * O (cos x) ^2 O 1 O (sec x)^2 tan x

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Q: How did he get the second derivative step by step and a clear line please 3 F(x) = 1+e siny x Fex)…

A: Let fx=1+e-xsin 4x

Q: Compute the derivative d tan x dx \cos x COS X 4 sec2 x – sinx tan x 1– 4 cos x + tan? x - | (cos x…

A: We have to compute the derivative of the given function: ddxtan xcos x-4 We know the formula of…

Q: Find f'(x) if f(x) = etan²x f'(x) = (2 tan x)etan²x f'(x) = (sec² x)etan²x %3D O Option 4 O Option 1…

A: In this question we have to perform differentiation.

Q: f(x)=πcos⁡(πx).  Find the twentieth derivative of f(x)

A: After third derivative, the sign will become positive because of the Cosine and the coefficient will…

Q: Find the derivative of y 3 sin x +5 cos x A. 3 cos x +5 sin x C. 5 cos x +3 sin x B. 3 cos x-5 sin x…

A: Differentiate wrt x

Q: Use Leibniz’s Rule to find the derivatives of the functions

A: Use Leibniz’s Rule to find the derivatives of the functions

Q: Find the derivative of: a. f(x)=ln(csc^2(x)) b. f(x)=ln|sec(5x)+tan(5x)| c. f(x)=(lnx^2)^2

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Q: Consider the function f(x) whose second derivative is f''(x)=2x+7sin(x). If f(0)=3 and f'(0)=3, what…

A: to find f'(x) integrate the given function c=integrating constant. Then plug x=0 and f'(0)=3 and…

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

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Q: If function f(x) is not continuous at the value x = a then the derivative of f does not exist at x =…

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