f f(2) = / cos(t) dt, then f'(x) = %3D COS Select one: a. 3e cos(a?) b. e cos(ez) c. 3e cos(e6z) d.e cos(z)

Q: y(x) = tan{/3x² + In(5x*) - In(5x'

A: Given  y(x) = tan3x23 + ln5x4 We have to find dydx.

Q: Calculate integration | cos -1 1 dx

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Q: dx (2) S V9-x² E(Ctrl) X. 2x sin-1(구)+ sin-1 (민 + Option 1 Option 2 2x cos-1(민 + c CoS Option 3

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Q: If y = tan(4x + 1), determine using chain rule. dy dx

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Q: cos² (6y) + sin²(6y) = y + 12.

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Q: Q3) Find dy/dx if 1- y= In x 2- y=x sinx+1-x

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Q: Let z= sin (y2 – 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: Estimate S, cos(4x)dx with Trapezoidal Rule. n = 10

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Q: Find the local linear approximation of cos x at xo = cos 61°. T/3 and use it to approximate

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Q: Find the derivative of cos(0)d0. du Jo cos(0)de = cos (w²) · 2w • d de So" cos(8)d0 = cos(2w) • d S…

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Q: If sin(5x - 5y + z) = 0, use implicit differentiation to find the first partial derivatives with…

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Q: dy tan tan x = 0 dx coscos x +

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Q: Ssint2x)dx = 2cos(2x) (2x) + С -cos(2x) + C O 2 cos(2x) -cos(2x)+ C

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Q: If f(x, y) = y cos(x) – x* In(y), find the second partial derivative (A dx? -y? cos(x) – 6x In(y) d…

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Q: dy/dx of y = (x^2)cos^4(x)

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Q: dy Cos(3x) + (In x)

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Q: in integrating the function fx cos() dx using intogration by parts, whut would you choose for your…

A: Solution

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: y + sinx cos2(xy) cos (xy) Ex. 13. Solve dx + %3D .cos?(xy) + siny ) dy = 0. CS Scanned with…

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Q: Find dy/dx of y=sin-!x+cos -!x dy/dx is Blank 1.

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Q: dy cosx+ ysin x =1 dx

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Q: Explain why the linear approximation to ƒ(x) = cos x at x = 0 is L(x) = 1.

A: The linear approximation, or tangent line approximation, of f at x=a is defined as Lx=fa+f'ax-a This…

Q: Find dy/dx if y= cos-1 In(x+1)

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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: Integrate: x² cos(2x) dx

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Q: determine dy/dx if xy = ecsch(x)+πcos(0)

A: Given, xy = ecsch(x)+πcos(0)

Q: Ssin (2x)cos(2r)dx

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Q: Find the solution of the equation in the interval 0"sx <360 1. cos x+) 3 = - cos x +T3%3D

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Q: Find dy/dx by implicit differentiation. 3 cos (9r) sin (2y) = 8 dy/dx =

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Q: (5) Find the derivative dy/dx, where: 4 1 -1 y=- y = cosec(cot3x), y=Vsinh¯3x 3 1+ cos° x

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Integrate: / cos“ x dx

A: The given integral is: I=∫cos4x dx Reduction formula: ∫cosnx dx=1ncosn-1(x) sin(x)+n-1n∫cosn-2(x) dx

Q: 4. Evaluate: a) 4 (earctan x)dx o dx b)음 arctan x dx # earctant dt

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: A particle, initially at rest, moves along the x-axis such that its acceleration at time t &gt; 0 is…

A: Given acceleration, a(t)=cost,       t&gt;0 And v(0)=0, x(0)=3

Q: It can be shown that the Difference Quotient (D.Q.) of f (x) = sinx is h-[sinx(cos(h) – 1) +…

A: We are provided that the Differential Quotient (D. Q.) of f(x)=sinx is h-1sinxcosh-1+cosx sinh, if…

Q: Find dy/dx for 4 cos4 xsiny = 15

A: d(uv)dx=udvdx+dudxv

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: In integrating the function fx cos(3x) dx using integration by parts, what would be your v?

A: Solution

Q: In integrating the function fx cos(3x) dx using integration by parts, what would you choose for your…

A: Let ,I=∫ xcos3xdxSubstitute  u=3xdifferentiate du=3dx⇒du3=dxI=∫ u3cosudu3I=∫ucosu9duTake the…

Q: In integrating the function f(3x + 5)(cos ) dx using integration by parts, what would be your du?

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Q: S" cos de 4. 2 dx .2 -1 1+x² 5.

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Q: A particles velocity is 7 cos(2t) meters per second. at time t=0 its gone  2meters, where is it  at…

A: The velocity of the function is given as:

Q: A population x of rats satisfies the DE dx /dt ka?. Initially there are x(0) = 2 rats, and their…

A: The general solution of a differential equation always contains a constant of integration. The…

Q: Find at the point (1,0) for cos xy + ye* = 0. dx

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Q: b) Find if e Vt2 +5 dt + siny = x- xcosy rsinx ycscx

A: According to Leibniz' rule:

Q: Find the value of dy/dx at the point (−2, 1) for the function which is defined implicitly by

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Q: (a) f* (1 – cos 3t) sin 3t dt,

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Differentiate implicitly to find dy/dx. cos(x) + tan(xy) + 4 = 3

A: Given: cosx+tanxy+4=3We need to find dydx.Recall the formulas: ddxcosx=-sinx…

Q: The derivative of : y =0(sin (In (0))) + cos(Im (0)) is:

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Q: 5) ( cos 'x dx -1 Where: u = cos(x) dv = dx

A: