Calculate dz/dt given the following functions. Express the final answer in terms of t. f(x, y) = x²-3xy + 2y², x = x(t) = 3 sin 2t, y = y(t) = 4 cos 2t Z=

Q: 3x4-4 cos x = -6

A: Find d2y/dx2 implicitly in terms of x and y3xy − 4 cos x = −6

Q: Integrate {w^7 * cos(3w^4)dw

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Q: 1 -dx = /8-(2x+5)² o įsin- (2*) 2x+5 + c V8 2x+5 sin-1 + c 8, tan- ( V8 2x+5 + c o ţtan" (2*5 ) + c…

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Q: y'tan x sin 2y = sin² x + cos² y.

A: We need to solve y' tanx sin2y=sin2x+cos2y This can be written as: y' tanx…

Q: how does dy/dx(tanx) become sec^2x

A: It is a standard derivative formula, whose derivation can be found mentioned below.

Q: (xy^2+y)dx -xdy =0

A: Given: (xy2+y)dx-x dy=0

Q: Question 5 Evaluate the Integral / costx sinx dx (A 5 -cos x+C (B) -sin³x+C -sin*x+C -cosx+C D

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Q: e5x cos e5x dx sin²e5x

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Q: Evaluate dy/dx at the point (π/2, π/2), if 2 sin^2 x + 1/2 cos y = (3 sin x)^11 . Mention all…

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Q: integrate (cos (x)/(sin(X)-cos(x))

A: Integration is a technique of finding a function  the derivative of which, , is equal to a given…

Q: Integrate fx cos(4x) dx fa

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Q: العنوان solve b sin ² (3x) cos² (5x) dx 2 8 tan³x dx >

A: First, we need to identify the type of integral we are dealing with. The first integral is a product…

Q: (a) [- 9x2 +x° cos x dx = 3

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

Q: | 1' cos(T +1) dr. COS

A: using the integration by parts

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: 5. 4 (secx-1)(sec² x+secx+1) Sª cos² 2x-2 cos 2x+1 -dx

A: Indefinite integral is the process through which one can determine the function which on…

Q: We know that a= 23 sin' (ax) cos(ax) dx = sin³ (ax) b Find b + C

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Q: Let 5 sin⁡x+ 7 cos⁡ y=6. dy/dx= d^2y/dx^2

A: 5sinx+7cosy=6Differentiate w.r.t x5cosx-7sinydydx=05cosx=7sinydydxdydx=5cosx7siny

Q: dy Find if y = 4 sin?(3x) dx

A: Here we have to find the derivative of function y which is given as above. Here I am attaching a…

Q: Find d²y/dx² if y = =x cos(3x) — sin²(x). -

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Q: y = cos((TX)5)

A: Please see the white board.

Q: Find if cot x +1 = sin y

A: Given, cot x + 1= siny

Q: +3x2, (V)² = sin³(cos³(*3**» dy b. Find dx %3D

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Q: Solve the equation [cos (2y) - (3x^2)(y^2)]dx +[cos (2y) - 2x sin 2y - (2x^3)(y)]dy = 0

A: To solve the given differential equation. First we check whether the differential equation is exact…