(a) Let f(x) = cos(3x – 2). Find f"(x). (39) %3D (b) Let g(x) = 2***. Find g (153) (x). %3D

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Q: Find the third derivative of f(x) = ³/15z + 1. f"" (2) - ab a b √a |a| π sin (a) 2.

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Q: Estimate the instantaneous rate of change of f(x)= cos(x-7)+4 at x = π. a) 4. Ax =4 b) Af =1 Ax Oc)…

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Q: dy Q1: Solve the DE x3 dx3 +x = x Inx cos(2lnx) by using inverse dx operator method.

A: Given differential equation is .....1 Its solution is given by yx=C.S + P.I ; where C.S is…

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Q: Solve th D.E using Exact dx +(x² +3y* )dy

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Q: 6. f(x) cos (4x- 16), when x = 4 (0 in the given function is in degree measure)

A: Given- fx=cos4x-16 To Find- The value of the above expression when x=4 and θ in the degree measure.

Q: The derivative of the function y = (3e* – x²)(cos x) is: a) y' = (3e* – 2x) cos x – (3e* – x²) sin x…

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Q: (1) (a) Find the derivatives of functions f(x) = e2 and g(x) = 5æ?. (b) Compute the definite…

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Q: 2- Find dy/dx for y = In(tan(2x2))

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Q: Let z=sin (y 2- 4x). Find the rate of change of z with respect to y at the point (2, 1) with x held…

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Q: Some elementary functions, such as f(x) = sin(x2 ), do not have antiderivatives that are elementary…

A: let ∫x-necxdx for n a positive integer and c a non zero constant is non elementary since…

Q: (b) by using gamma function x-1/3e-Bx dx

A: Gamma function

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A: Given that, y=cos4(4x2-3x+1)

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A: Given that: y=sin-11x3

Q: Let z= sin (y²– 4x). Find the rate of change of z with respect to x at the point (2, 1) with y held…

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Q: Find dy/dx: y = sin (In x²). A 2 cos (In x²) (B) 2 cos (In x²) / x

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Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x*+1) 3- xy + x²y = 3 at x = 1 4-…

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Q: If y = sin (4x - 5), then what is y' a. y = 4 cos (4x - 5) b. y 3 сos (4x - 5) C. y' = -cos (4x) d.…

A: In this question  we have to solve the given statements. NOTE: As per our policy we are suppose to…

Q: determine the annihilator of the givenfunction. F(x) = x cos 3x.

A: Consider the given function, F(x) =x*cos 3x. Let f(x) is a function, which is defined as,…

Q: Find the antiderivative of f(x)=cos(3x)

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Q: Find dy dx' i) f(x) = Cos2x Sin²x %3D ii) f(x) = log,(x' +4)* e-* /2x - 5 -3x iii) f(x): (6-5x)'

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Q: 5. y = l 1- co s x 1+co s x

A: We have to find out dy/dx for given y

Q: the chain rule - find dy/dx (derivative) of y= (4x11 + sin(5x))1/8

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A: Given : sin12x+7

Q: (a) By using the chain rule and the derivative = (xl) if x>0 (-1, if x< O' dx find - (Ix – x|)DvxE…

A: Given : ddx(x)=1 ,     if x&gt;0-1 , if x&lt;0 To find : ddx(x3-x) , where x∈(-1,1) and x≠0

Q: Ssin^3 (2/3 x) cos^4 (2/3 x) dx

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Q: find dy/dx. y = x2 cos x - 2x sin x - 2 cos x

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Q: (a) Determine f 2xe3*dx by using integration by parts. (b) Determine S cos(x²) 2x dx by using…

A: Given,  ∫2xe3xdx ; We have to integrate using integration by parts ∫cosx22xdx ; We have to…

Q: Find values for the constants a, b, and c that will make ƒ(x) = cos x and g(x) = a + bx + cx2…

A: Consider the following functions: fx=cosxgx=a+bx+cx2 f0=g0cos0=a+b×0+c×021=a+0+0a=1 Hence, the value…

Q: Find dy/dx of y=sin -1(1/x). (A x²– 1 3 B 1- 9x2 1 9 D 1-x2

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Q: :- x2 + 10x + 24 dx. 1+ cos2 (x) f(t) = %3D At what value of t does the local max of f(t) occur? t =

A: Given: ft=∫0tx2+10x+241+cos2xdx

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Q: find dy/dx. g(x) = cos x/sin2 x

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Q: 4. Find the indicated higher-order derivative of the given functions. d'y а. у %3D 8е* + sin x; dx7…

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Q: Q1) find dy/dx 1) F(x) = sin’2x tan x² x – 3 ) 2) F(x) = sin( x +4

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Q: (c) Find dy/dx by implicit differentiation cos(x² y) = x

A: We are given, cos(x2y) = x We need to find dy/dx

Q: What is the process for finding dy/dx when y is an implicit function of x? Illustrate with an…

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Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x+1) 3- xy + xy = 3 at x = 1 4- y…

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Q: 37 a)/ 2x cos(x) dx he right end-points with 4 sub-intervals) 1 b) -2x2+ X-4) dx 5.

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Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x+1) 3- xy + x²y 3 at x = 1

A: Here, We need to find the derivative of the given functions. To solve these questions, we need chain…

Q: a. f sinx cosx √1+cos2x dx x√x x³+1 dx b. f*¹+¹ dx c. f x²

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Q: Find the 1st and 2nd derivatives of the following profit function: =(xa-110)1/a that is, and find…

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Q: 2- find dy/dx e2x = sin (x + 4y) 3-find an equation for the line tangent to the graph f(x) = x –…

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Q: Find the third order derivative of y = In(cos(2x)). A. y' = -40sec? (2x)tan(2x) B. y' = -80sec?…

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Q: Let -sin (y-4x) Find the rate of change of z with respect to y at the point (2, 1) with x held…

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