t y(T) dr = 4te¯t, y(0) =

Q: Find the differential dy: y = In (sec² (3ª²–2x+5)).

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Q: Find the general solution of

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Q: t2 + 4t + 10 -dt t3 + 2t² + 5t dy J 3 + 5cosy

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Q: Find the differential dy. y = 5x2 / x-9       dy =

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Q: find dy/dt. y = ecos2(πt-1)

A: We use the chain rule to find the derivative

Q: dy J- (1+x)+y = 1+t dx

A: Note: since you have posted multiple question. As per our guidelines we are supposed to solve one…

Q: dy dt t2

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Q: Find the differential dy, then evaluate: y= 2x3+ 6x-| when x= -2, dx= 0.l

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Q: dx – x = 4y, UTM dt dy + x = y + 3e', dt

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Q: b- Yt dt + dBt dY; 1-t

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Q: If x =t-1+5 and y 6+t-2 then dy at t = dx is

A: topic - derivatives answer is 4

Q: Find dy/dx and d2y/dx2 of x= t + 1/t, y= t + 1

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Q: Find the differential dy of the given function.

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Q: 9. Sinte)e x(t² + 1)dt = x ,(t² + 1)dt S' 2* dx < S, xdx 10. dx = dx + dx 11.

A: 9.∫ln(e)0ln(e)ex(t2+1)dt=x∫0e(t2+1)dt10.∫012xdx≤∫01x dx11.∫131xdx=∫151xdx+∫531xdx

Q: (a) Find the differential dy. y = 1/x+1

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Q: Find dy if x=t+6f and y= dx 2 5 at t=1 +

A: We have to find dy/dx

Q: Let y = 5x?. Find the change in y, Ay when a = 3 and Ax = 0.3 Find the differential dy when x = 3…

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Q: dx at x = dt dy Find - 5 if y = x² - 3 and = 4. dt

A: A detailed solution is given below

Q: 3y" (t) – / (t) = e' cos(t) + sin(t), y(0) = 0, y'(0) = 0 -

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Q: find dy/dt. y = (esin (t/2))3

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Q: dx at x = dt dy - 22 – 2 and dt – 5 if y = 4. Find - dx dt

A: We will find the derivative.

Q: d Evaluate In(et – t²)dt. Briefly explain your answer. dx '1

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Q: Q4) Use the chain rule to express dy /dx in terms of x and y t2 y = t2+1 and t = 3x3 – 3 where x =1

A: Given y=t2t2+1 and t=3x3-3 and x=1

Q: Find the differential of the function. y = V6 - t8 dy %3D

A: Solution: The objective is to find the derivative of the given function

Q: 2. Find dy/dx a) y = dt, x> 0

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Q: y dx + x(Inx-Iny -1) dy z

A: Use substitution lnx=u:…

Q: 크(F(a+) e dt dx 19

A: We have to evaluate, ddxFx4=ddx∫10x4  e-t2 dt

Q: Find the differential dy of the function y = Provide your answer below: dy = dx 5x4 + 4 4x + 3

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Q: x' = 1 t + 8' dy 4e-21, dx x' = tsin t², = x(1) = 0 y (0) = 3 x (0) = 1

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Q: dy Find dx x2 y = dt dy dx (Type an exact answer in terms of e.)

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Q: %3D y"(t) = 4y(t) – e-tU (t – 1), y(0) = y'(0) = 0.

A: Solution

Q: y1(t) 6y/(t) + 8y(t) = e2t + sin (t) ; y(0) = 0 ; yr(0) = 1 -

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Q: dr = x – y +t dt dy =エ+3y +t+1 dt (20, yo) = (-4, 5)

A: Given that, dxdt=x-y+tdydt=x+3y+t+1 This can be written by, X'=1-113X+tt+1 Now the homogenous eigen…

Q: a) dx dt dy dt =x+√3y+et √3x-y+e³t = ||

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Q: Let y = 3x² + 8x + 3. Find the differential dy when x = Find the differential dy when x = 2 and da 2…

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Q: Let y = (x² + 3)². Find the differential dy when x = 5 and da = 0.2 Find the differential dy when x…

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Q: Find the differential dy of the given function. y = V 3 - x2 dy =

A: Find derivative

Q: dx T2 +2 and dt dy 2. Find at I = 2 if y = dt dy dt

A: Solve for dy/dt at x=2

Q: Find the value(s) of dx at y=1 given that x²y+ y² = 5.

A: Given,        x2y+y2=5  and dydx at y=1

Q: Find the differential dy of the function y Provide your answer below: dy= dx = 5x4 + 4 4x + 3

A: y=5x4+44x+3Differentiate w.r.t xdydx=4x+320x3-5x4+444x+32

Q: se the Chain Rule to find dw/dt. w = INVX2 + y2 + z² x = 9 sin(t

A: Here we have to use the chain rule to find dwdt=? w=lnx2+y2+z2, x=9sin(t), y=3cos(t), z=5tan(t)

Q: d²y dt² d'y 11. + (cos t)- dt4 +y=e=tsin t

A: Given - d4ydt4+(cost)d2ydt2+y=e-tsint To determine whether the given differential equation is…

Q: dw Q11- express by using the chain rule: dt w = ln(x² + y² + z²) x = cost, y = sint, z = 4√t

A: We have to express dwdtby using the chain rule:

Q: Find the differential dy. x + 2 y = 9x - 1 dy =

A: In this question we have to find we have differentiation of y.

Q: dy dy + 7 dt + 10y = e-t dt2

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Q: d rIn(x) t tan(t) dt|. dx -1

A: we have to evaluate the following

Q: t y + 4y + 3√ y(t)dt = 6-7 e²₁ y(0) = 1

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Q: y sin (r²) dt

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Q: C. dt² +y" = 0 dy d. xty" + ху" 3 е* e. t2 dt2. t2 ( - t = 1- sint е.

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