1. Find the domains of the following functions. x2 - 2x 2.x-3 (a). f(x) = (b). f(x) = (c). f(x) = 3 sin r+5 tan r %3D x2 – 5x +6 Vx2 - 5x +6

Q: 1) Find the second derivative for the following functions: a) f(x) = 4x³ + 3x² + x – 14 b) f(x) =…

A: Solve derivative a fx=4x3+3x2+x-14b fx=4x-3+2x-4c fx=5ex-e3x

Q: 1. Determine the particular solutions of the following function. (D3 – 3D – 2)y = 0; when x = 0, y =…

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Q: 1. a) Find the successive derivatives of the following functions: (x' +80x²)* ii) Z (x* +10x +20) 21…

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Q: 4. Find the second derivative for the following functions : a) y=(x+!)' (ans.:6x +6+ 12) x' b)…

A: (a)

Q: Find the first derivative for the following function. Vx4 – 3 (2х — 5)"] f(x) = ln (2x-5)7 Vx4-3 2x3…

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Q: 12. Given the function y=6x-2, find the derivatives O -6 O 2 O -2 Required

A: Topic:- calculus

Q: Suppose that the function ƒ(x) and its first derivative have the followingvalues at x = 0 and x =…

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Q: find the derivatives of the following functions f(x)=(3x2 +5)2(x3-11)4 f(x)=COS4(x+1/x-1)

A: 1st question :Given,         f(x) = (3x2+5)2(x3-11)4

Q: 1. Find the derivatives of each of these functions: a. y = ln (4x² + 4) b. y = 22² c. y = 25x+7…

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Q: (a): Find the value of k that makes function continuous at x = 4 f (x) = 7x S2x + 7 x > 4 k x < 4…

A: We will use the definition of continuity at a point to find the value of k

Q: 1. Find T3(x) and R3(x) for the function expanded about x0. (c) f(x) = sin(x); x0 = pi.

A: The nth partial sum of Taylor series for f(x) is given by, at x=a Tn(x)=∑…

Q: 11. Suppose that the equation g(x, y, z) = 0 determines z as a differ- entiable function of the…

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Q: c) h(x) =(5x-1) 12x² – 6 d) m(x) = (4x² – 9x} %3D

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Q: True or false: The maximum value of the function y = -2 cos x + 5 is 7.

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Q: Find all critical points of the following function. 3. 3 f(x.y)=- + 8xy

A: To find critical points of f(x, y) we find ∂f∂x and ∂f∂y then equate to zero .f(x, y ) =…

Q: True or false: The maximum value of the function y = -2 cos x + 5 is 7.______

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Q: Find the derivatives of the following functions. f(x) = (-2/3)x - (1/2)x? + 9x f(x) = f(x) = x* sin…

A: We will use following formulas of derivative to find Derivatives of Given function. ddx(UV) =U…

Q: B. Find the first and second derivatives of the following: 1. m(x) = 2(x)(√x) 2. a(x) = √3x 3. [u(x)…

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Q: 10. Find the derivative of the following function. [Hint Using Chain Rule] a) F(x) = (x³ + 4x)7 d) y…

A: The chain rule says:ddx[f(g(x))]=f'(g(x)) g'(x)=d[f(g(x))]d[g(x)]·d[g(x)]dx   Note: According to the…

Q: Use the theorem of Leibniz in the following problems: 1. Obtain the n'th derivative of: x2y [x?y") +…

A: The objective of the question is determine the nth derivative of the given equation.

Q: Q1-Find the derivatives of the following funetions using the defir 1. y=x-x 2. y-3/5х 3. y=x 4.…

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Q: Find the derivative for the following functions: a)f(x) = log4 x + 6x² + J¤ 1 5 1 12x + f'(x) = x In…

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Q: The action of a waterwheel can be modeled by the function y = 3 cos(T (x - 3) + 2). Within the…

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Q: Find the indicated derivatives for #'s 1-6: 1. y'for y = 4In x 2. f'(x)for f(x) = In x³. 3. a. f'(x)…

A: As per guideline we have to solve three question

Q: 2.4 Use the definition of the derivative of complex function to show that f(2) is not dif-…

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

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Q: 2. Find the derivatives of the following functions and simplify. i) f(x)=- Vx +1 ii) h(x) = In(x+…

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Q: Q1 (a) Use partial differentiation to determine the expressions for in the following cases: ôx (i)…

A: Explained below

Q: 4. Find the second derivative for the following function a) )* 22 y3(x+ (an b) f(x)=/2x + at x= 2 c)…

A: See the attachment

Q: Find the first derivative for the following function. g(x) = 4e3x*+2x %3D A. g'(x) = 4e3x*+2x +…

A: Given function: gx=4e3x5+2x Differentiate the above function w.r.t 'x' g'x=ddx4e3x5+2x

Q: 1. Find the derivatives for the following functions. x3 A.f(x) = (3 Inx – 1) | t2 +t3 +1 В. f(t) %3D…

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Q: 59. Suppose that functions f and g and their derivatives with respect to x have the following values…

A: Since you have posted multiple questions i can do first question with first three subparts as per…

Q: Question 2. Find the critical points of the function g(x, y) = x²y + 4xy.

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Q: 1. Find the first derivative of the following functions: y = f(x) = -(2x + x³)-2 + 4x (2x+4)² (a)…

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Q: Suppose that functions f and g and their derivatives with respect to x have the following values at…

A: Note: Since we are authorized to answer three sub-parts of a question at a time. And you have asked…

Q: 6.) Find the derivative of the following functions a.) f(x)=- 7-3х |t +1 b.) f(x)=. -1 c.) f(x)= ean…

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Q: In(4x Given f(x) = the derivative f'(x) is 4 1 4x 1 4x O 4 O z4z

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Q: 1. Determine the third derivative of the following. A. f(x) = x³ – 4x² + 5x + 3 B. f(x) = Inx [ K:…

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Q: Q3. Discuss: max f(x), where f(x) = cos.x . (Start with a graph of the function, and confirm your…

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Q: Consider the graph of the function given in the image: Knowing that L {x (t)} = X (s). Find X (s)…

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Q: 1 Let f(x)=- (3x – 5)² -6 and f'(x) = %3D (3x – 5) Find an equation of the line tangent to the graph…

A: The given function is: f(x)=1(3x-5)2

Q: Sketch a graph of the function f(æ) = – sin(x). -T/4 T/4 /2 3n/4 5t/4 3n/2 元 7/4 -1

A: Given: A function, fx=-sinx. -sinπ4 -32 -sin0 0 -sinπ2 -1 -sinπ 0 -sin3π2 1 -sin2π 0…

Q: Match the functions in Column A with their derivatives in Column B. 1. f(x) = 4 А. f'(x) = 8x 2.…

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Q: 1) A course repeater claims that his brother who did some Calculus at college years ago, but…

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Q: Find the derivative. y= e at O 4(1/4)x -4(5/4)x In 4 4(3/4)x In 4 4(5/4)x 25 n4 16

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Q: Q3) Draw the following functions: (2-2x, x 3 1)f(x) = 2)y = -sin 3

A: Given: The functions are given as 1) f(x)=2-2x,x&lt;-14, 2x-2-1≤x≤0x&gt;3 2) y=-sinπx3   To graph:…

Q: I. Find the derivatives of the following functions: 1. f(x) = v2x4 + 3 2. f(x) = (2 x² + 5)-ª (4 x5…

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Q: Find the first derivative for the following function. g(x) = 4e3x*+2x %3D A. g'(x) = 4e3x*+2x +…

A: to find:- first derivative of g(x), i.e. g'(x). *formula:- d/dx {e^x} = e^x d/dx {x^n} = n*x^{n-1}

Q: Find the derivative. COSx a) f(x) = In %3D x2-4 4 b) g(x) = Vx + e2x + Tt

A: Given : (a) f(x)=ln(cosxx2−4)

Q: Find all the higher derivatives of the function f(x) = (3x+7)°. TATER P'(x) = P'(x) =] p"(x)=

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