The function f(1)3 sinh(In()) Is equivalent to which of the following functions Select one

Q: Derive the following function 8. y = tanh-1(sinx)

A: We have to find  the derivative

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: Suppose we define a function f(x) by f(x) = a1 sin(x) + a2 sin(2x) +· + an sin(nx), .. for constants…

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Q: 3. Find the derivative of the following functions using the definition of the sine and cosine…

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Q: if f(x)=ln(1+cosx) then find f`(x)

A: f'(x)=(1+cos(x))'/(1+cos(x))      =-sin(x)/(1+cos(x))

Q: ) = 5 + 4 sin(x). If f(0) = 3 and f' (0) = 4, what is f(x)? Consider the function f(x) whose second…

A: Given:

Q: Which of the following functions is/are TRUE? A sinh(-x) = -sinhx B cosh(-x) = coshx tanh(-x) = -…

A: topic- hyperbolic functions we know that sinh(-x)=-sinh(x) cosh(-x)=cosh(x) tanh(-x)=-tanh(x)

Q: 3. Find the derivative of the following functions using the definition of the sine and cosine…

A:

Q: 1 3.| y = xSin(x) + (1 – ÷x²) Cos(x) (1-**) Cos(x)

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Q: -1 We can conclude from the derivative of sin-1(x)and cos-1(x) that sin-(x) + cos¯(x) is constant.…

A: Explanation: find the derivative of sin-1x & cos-1x

Q: Find the derivatives of the following from first principle: f(x) = sin( 3x - 4 )

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 2. The height of a toy that moves up and down on a spring can be modeled by the function y = – cos x…

A: sin 2x =2sin x cos x

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

A:

Q: (A) Find an equation of the tangent line to the graph of f(x)=(4x+1)sin(πx) at the point whose…

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Q: 5. Find the derivative of each problem below, do not simplify. tan(2.x) f (x) = x² +2 а. b. f(x) =…

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Q: Solve for the derivative of the given functions using the Chain Rule formula. Suppose f(x) =…

A: Given: f(x)=sin(2x)+17 To find: f'π2 and f'(π)

Q: Find the absolute extreme values of the function on the interval

A: Refer to the question we have to find the absolute extreme values of the function provided on the…

Q: Solve for the derivative of the following functions. Write your answer on a separate sheet of paper.…

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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: 3. Find the derivative of each of the following functions. Justify your answer. (a) f(x)= (b) y e I…

A:

Q: Let k(x) = tan−1 x. Find the value of k(9)(0), the 9th derivative of tan−1(x) at x = 0.

A: Given

Q: 1. Find the derivative of the following: (Simplify your final answers.) f(x) = ev3(cos²zx) C.

A:

Q: 6) Find the derivative of the following functions 6.1) a(x) = x²(sin x)(cot x)e" 6.2) b(x) = ()-4

A: To find the derivative of the following functionsFormula:ddx(sin x)=cos xddx(cot x)=-csc2…

Q: Let f(x): e² sin³ (4) x6 sec(x − 2) a. Solve for f'(x) without using quotient rule or product rule.…

A: As per the question we are given the function f(x) and we have to find its derivative f'(x)  without…

Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Given :             cosh(3x2y) = x + ln(exy + 1)   To find :            ∂y∂x

Q: The derivative of the function y = 9 sin + 22 is. 0 + (In 2") O - (In 2)2= O + (In 2)2" 0로+ (In 2)2"…

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Q: Find the derivative of the function. f (x) = 4/3 Squareroot x + 4 cos x Rewrite the function f(x)…

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Q: Use the following derivative function f' to determine the local minima and maxima of the function f:…

A: Consider the provided question,

Q: 6. Find the derivative of the following (express answer in simplest form): 1+ sinx a. f(x) = In…

A: Topic = Derivative

Q: Here are three functions involving exponential functions: s(x) i) s(x) = 글 (e" -e") i) c(x) = } (e*…

A: Introduction: The trigonometric functions are also differentiable over their principle domain. The…

Q: 4) u = x² sin=1 x 5) Ø = tan¬1 3 0 6) y = In(7 – 3x)

A: This question is taken from the derivative in which we have to find the derivatives of the given…

Q: Consider the function f(x) whose second derivative is f"(x) = 10x + 10 sin(x). If f(0) = 4 and f'(0)…

A: Given that: f''(x)=10x+10sinx

Q: The function f is defined by f(x) = x² + 2 cos (3x + 3x). What is the average rate of change of f'…

A: Average rate of change of a function f on [a,b] is given by f(b)-f(a)b-a. Computing f(10) and f(3).…

Q: 5. Given b(x) = (3x – 7)*, if m(x) = 36 (2 tan-1 (1 – 7x)) then m' (x) is %3D %3D

A:

Q: Find the derivative of the given function. COS ³ (1) g(x) = 2 cos3 O a) g'(x) = -3 cos² (sin() Ob)…

A: Given, g(x)=2 cos3x2

Q: Sketch, on separate graphs, each of the functions : (i)sinh(x). (ii)cosh(x). (iii)tanh(x).

A: Hyperbolic functions: These functions are defined as the algebraic expressions of the exponential…

Q: Q3/Discuss the behavior of the following function as x 0: f) = sinx

A: Please rate and feel free to ask any query about any part of the question

Q: 1. Find the derivative of each of the following functions a) f(x) = cos5x %3D b) g(x) = cos 5x c)…

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Q: Find exact value(s) for x such that 3e" - e' = 0.

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Q: Solve for the derivative of the given functions using the Chain Rule formula. a.) Let f(x) = √(x2 +…

A: Solution

Q: Which of the following expressions is 1009th derivative of g(x) = -2 sin x ? g(1009) (x) = 2 cos e…

A: Given, g(x)=-2sinx

Q: 3. Prove that: cosh x - sinh x = e¯*

A: Proved Coshx - Sinhx = e-x

Q: 7. Find the second derivative given g(x) = sin x² A. 2(cos x? – x sin x?) B. 2(cos x? – 2x² sin x²)…

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Q: 6. Take the derivative of the following function and simplify as a simple fraction which cos x does…

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Q: 1. Compute the first, second, and third derivative of a. f(x) = x² In(x+1) b. h(x) = x² sin x

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Q: calculate the value : f'(x) 3. a) f(x)=4xe**+ln(sin/x)+2cos(x³ +2x+1)

A: f(x) = 4xex3 + lnsinx + 2cosx3+2x+1f'(x) = ?

Q: Consider the function g defined by 1 g(x, y) = cos (7x/) - CoS log3(x – y)

A: Given problem:-

Q: Differentiate each of the following functions with respect to x. 1. y = In cosh2x 2. y = e" sinh x…

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Q: Let f (x) = x sin x and g(x) = x cos x. (a) Show that f ,(x) = g(x) + sin x and g ,(x) = −f (x) +…

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Q: In finding the root with Newton's Method, an initial guess Xo = 4 with f(Xo)= 1 leads to X1 = 3.…

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