dw Use the Chain Rule to find where w= cos 12x sin 4y, x=5, and y =t". dt dw dt (Type an expression using t as the variable.)

Q: sin (t) -dt 3 (4+ cos (t))?

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A: To evaluate the given definite integral

Q: Find the length L of the curve R(t) = -2 cos(5t) /+2 sin(5t) /+ tk over the interval [3, 6]. L =

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Q: 5 dx Find dx, x> V25x? -9 5x In 25x2-9 + C 3. sin-13x+c 1+9x2 +3x|+c 1 V1+9x? + C 3x 3. + C V25x2 -9…

A: The solution is given below in the next step:

Q: Homogeneous Find C, if y f(cos 2n) = tan 45° 3(3x + y?)dx-2xydy 0

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Q: dz dz Use an appropriate form of the chain rule to find and du dv х — 2 сos u, у %3 5 sin v Enter…

A: Solve the given

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Q: Find dy/dx, simplify if needed. y=sin^2(4x) + (1/2) cos 8x

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Q: (글) 2sinh -dx = Select one: O a. co cosh O b. (글) sech tanh d. csch

A: Properties used, a) Sinh (-x)= Sinh x b) Cosh (-x)= Cosh x c) ∫Sinh x dx= Cosh x +c

Q: i. L x² 8(x – a)dx ii. L,7t? cos t 8(t)dt L,7t? cos(t – 2) 8(t – 2)dt iii. -

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Q: dz and du dz Use an appropriate form of the chain rule to find dv z = -; x = 14 cos u, y = 17 sin v…

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Q: Eliminate the arbitrary constant/s of this equation to obtain the DE. Express the DE in general…

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Q: dw Use the Chain Rule to find , where w = sin 8x cos 2y, x= and y =t. dt dw dx (Type an expression…

A: Chain rule

Q: 26) y = tan((T/6)x) Period: TT. -217 -ㅠ TT 21T -2 -1 -1 -2 -ㅠ MCL @01 %24 ElN-

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Q: T/2 cos t dt 1 + sin²t

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Q: The integral (cos(3x)) sin(3x)dx under the change of variable u = cos3r becomes u du. Select one: a.…

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Q: (t² +3) cos(5t) dt

A: According to integration by parts:∫udv = uv _ ∫vduWhere u can be choose in the orderInverse, Log,…

Q: Q1/ Use the chain rule to find and when z = tan- (=) X = u cos V, du dv y = u sin v at point (u,…

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Q: dx = 1– cos(bx) Select one: a. br – In sec(bx) + tan(bx)| + C b. – csc(bæ) – cot(bæ) + C - - In |1 –…

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Q: (T/2 cos® x dx Determine the reduction formula for cos" x dx and then find

A: Given, ∫cosnx dx∫0π2cos6x The reduction for the above integral will be,   ∫cosnx dx=cosn-1x sin x…

Q: du = 3 and dx dy = cos u, find the du dy Given y = sin(3x – 2). If dx 3 cos(2x) 3 cos(3x) 3 cos(3x –…

A: Topic:- derivatives

Q: olve the following differential equations: {r cos²+ y sin2)y-{ysinž-x cosx = 0

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Q: dx. (a) [ cosʻ x+4 sin x (i) Evaluate Using the substitution ttanx

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Q: dz dz and dv Use an appropriate form of the chain rule to find du z = =; x = 16 cos u, y = 15 sin v…

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Q: Q3.a) Find if y + SE rsecx -dt = xy sint+1 dz Q4.a) if z = sin²0, and 0 = w² + cos (w) find-

A: 3a):  y+∫xsecx11+sintdt=xydifferentiate both sides and use Leibniz rule for differentiating the…

Q: dw Use the Chain Rule to find , where w = sin 8x cos 4y, x= dt , and y = t. dw dt (Type an…

A: Given w= sin(8x)cos(4y), x=t/2 , y=t3

Q: solve following differential by finding an appropriate integrating factor cosxdx+(1+2/y)sinxdy=0

A: Solution -  We have the given expression as -  cosx dx + 1+2ysinx dy = 0 1+2ysinx dy = -cosx dx…

Q: 5. x = cos 2t, y = sin 2t, 0 <t< T

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Q: 1 Find 는 dx by using chain rule, if f = u + u = T x , at x = = 4 cos?u

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Q: 6. Find * : y- + 5)ao TK, (b) y = Sin 5x I+cos 5x dx

A: Solving the problem by finding the derivative.

Q: 5-2x dy if y = cos Find dx %3D 5+ 2x

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Q: dz and du dz Use an appropriate form of the chain rule to find dv ; x = 16 cos u, y = 3 sin v Enter…

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Q: (c) x³ cos(x²) dx. (Hint: start by using appropriate substitution. an

A: the given integral is: ∫π2πx3cos(x2) dx we have to find the value of the given integral.   let the…

Q: The position at time t ≥ 0 of a particlemoving along a coordinate line iss = 10 cos(t + π/4). When…

A: Given,The position at  time t ≥ 0 of a particle moving along a coordinate line is s=10 cos(t…

Q: The integrating factor that can be used to turn the following non-exact equation into an exact…

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Q: dz when du Use the Chain Rule to find = e' cos 0 and r = 3uv, 0 = Vu? + v². sin A

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Q: dz dz and du appropriate form of the chain rule to find dv x = 14 cos u, y = 13 sin v rour answers…

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Q: cos e de =_ %3D • 2 • -T • 6

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2T -TT Evaluate: S. (sin x + cos y)dx dy II SII 71I

A: Let give integral is equal to I

Q: dz and du dz Use an appropriate form of the chain rule to find dv z = =; x = 16 cos u, y = 13 sin v…

A: In this question we have to find differentiation with respect to u and v.

Q: A ) Find ſ cos 5t dt B) If y = x² + , x = 2t -5 then find dt

A: A)-     I=∫Cos5t dtlet 5t=uderivating both sides5 dt = duSo,I=15∫Cos u du = 15 Sin u +C…

Q: 3-4K dx 4xス - oK t coS T

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Q: cos(5r)ő(1 – 3) dt = e sin(t)6(t – 2) dt =

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Q: dt cos?(t) dr dx du du + ex- at cos²(t) :-7u, ex dr du -7u dr t(0) = 0, x(0) = a, u(0) = e et heR.

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Q: Find dy/dx of: x3 - sin y = (1/x3) + tan-1 (ey) - π/4 Don't simplify the final answer.

A: Given:     To determine:

Q: Find dg(t)/dt 1+ cos t -1 8 (1) = sin t

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Q: 2 tan-1(y). x In(xyz), q ƏV when x = y = % = 1. ду Let V = eP cos(qr), with p = z cos(TY) and r = By…

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