If f(#) = | cos(t) dt, then f'(2) = s(t²) dt, then f'(x)%3= COS Select one: a. 3e cos(2) CoS b. e cos(e6z) c. 3e cos(ez) d. e cos(r) CoS

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

Q: if f(x)=2x-cos(x), Use Newton's method to approximate x, starting from the initial value xo=0

A: Solution:-    fX=2x-cosX           x0=0    f'x=2+sinxwe know      x1=x0-fx0f'x0           =0-f0f'0…

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

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Q: At time t = 0, then th

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Q: dy Find dx if y = cos (4x - 3x + 1) s*(4x²-3x + 1)

A: Given that, y=cos4(4x2-3x+1)

Q: 1. If F(x)= = cos a sin r (√t-1)' dt, find F'(x).

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Q: arctan(*) 1+e2kx dx =? A) arctan(e*)In|cos(arctan(e*)| + S in |cos(arctan(e**)dz]+ c kekx 1+e2kx B)…

A: ∫arctan(ekx)1+e2kxdxFormula to be used :1.Intergration  by parts2.Substitution3.ddxarctan(ekx) =…

Q: Use the appropriate form of the chain rule to find the derivatives. 12x2 + 12y2 + z²; x = p sin o…

A: Given:  w = 12x2+12y2+z2 x=ρ sinϕ cosθ, y=ρ sinϕ sin θ, z= ρ cosϕ  Find: ∂w∂ρ, ∂w∂ϕ and ∂w∂θ Chain…

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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…

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Q: Given the function f(x) = e-3x cos 3x, x = [0, 2π]. When is the rate of change of f(x) a maximum?

A: Here, the given function is: f(x)=e-3xcos(3x) Now, the rate of change is given by: f'(x)=e-3xddx(cos…

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

Q: Let y = tan(4x + 3). Find the differential dy when x = 3 and dx = 0.3 Find the differential dy when…

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Q: A particle moves in a straight line and any time t seconds, its velocity v m/s is given dx by e-".…

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

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Q: Let y = tan (3x + 3). Find the differential dy when x = 3 and dx = 0.4 Find the differential dy when…

A: Given is the function y=tan(3x+3) We need to find the differential dy when x=3 and dx=0.4. and…

Q: Let y = tan(5x + 6). Find the differential dy when x = 5 and dx = 0.2 Find the differential dy when…

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Q: Find the derivative. d | dx + 0 OA. x³ sin (x¹) +5, ○ B. sint dt C. 4x³ sin (x4) - cos (x4) - 1 D.…

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Q: If z = xy and x = e=' and y = sin(t), find the following derivative using the chain rule. Enter your…

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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…

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Q: Find dx (e3t + 1)dt. -cos(3rx)

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Q: Find the third order derivative of y = In(cos(2x))". A. y' = -40sec²(2x)tan(2x) B. y' = -80sec…

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Q: find / sin³ x cos³ x dx cos³ 2x sinº 2x dx 11. 12. cos² x dx sin? x dx 13. 14. 16. 7 sin y dy 7 cos'…

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Q: Find the third order derivative of y = In(cos(2x))5. %3D A. y' = -40sec² (2x)tan(2x) %3D В. у' 3…

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Q: Let y = tan(3x + 4). Find the differential dy when x = 4 and dx = 0.4 Find the differential dy when…

A: We know that, ddxtanx=sec2x We have,  y=tan3x+4 On calculating derivative with respect to x, we get…

Q: 2. In each case, find the derivative d. (a) z = x³ – y² and x(t) = cos 2t and y(t) = e-3t, (b) z =…

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Q: of y = In || dx 4 1-cos x 1. 1+cos x Find the

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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: 3. dy Find if y 2xy - x: dx = cos X using implicit differentiat

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Q: Show that d/dx(ln kx) = d/dx(ln x), where x > 0 and k is a positivereal number

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Q: dw of w==+ dt x. y Use the chain rule to find the derivative with x = cos 1, y = sin ?t, z = - dw…

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Q: Find (dy)/(dx) if ey = ex + sin(x2x).

A: Given ey=ex+sinx2x

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

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Q: Let y tan(3x + 2). Find the differential dy when x = 4 and dæ 0.2 Find the differential dy when a =…

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