Find dt y = 6t + /9+ 7-t dy dt |3|

Q: 3. Find (6-+- vē)dt Vy 4. Find S- dy (4-yの?

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Q: Find both first partial derivatives. 18y2 x az %3D ax dz ду

A: The given function is:z=18y2x

Q: x2y3-y=x+x2 find dy/dt

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Q: dx dy Find at x = 1 if y = – 5x´ – 3 and 5. - dt dt dx dt

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Q: Suppose ry 1 and dy -2. Find dt dx when x = 1. dt %3D dx %3D dt

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Q: d²x dx 2 + 10x = e2t x(0) = 0, x'(0) = 1 %3D - dt2 dt

A: Given differential equation is d2xdt2−2dxdt+10x=e2t. and x0=0, x'0=1 Write the auxiliary equation…

Q: 1-dt 3- Ln(t) dt. Q10:- Calculate dx J2x t2

A: Use fundamental  theorem of calculus

Q: If x2 + y2 = 25 and dx/dt = -2, then what is dy/dt when x = 3and y = -4?

A: Given x2+y2=25Differentiating with respect to t,ddtx2+y2=ddt25

Q: Find dy/dt if y=ln(t^2+1)/(squareroot of (4-t)

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Q: Which of these gives an integrating factor for dy 2ty = 3t + 1 dt -

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Q: Find both first partial derivatives. z= 4y?V dz az ду

A: We can solve the problem by partial derivative method.

Q: If x^2 + y^2 = 25 and dx/dt = -2, then what is dy/dt when x =3 and y = -4

A: Given that  x2 + y2 = 25   .... (1) dx/dt = - 2 To find dy/dt when x =3, y = - 4

Q: If y=x^4−5 and dx/dt=−1, find dy/dt at x=−3.

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Q: If x2y3 = 4/27 and dy/dt = 1/2, then what is dx/dt when x = 2?

A: Given:

Q: ..... Find both first partial derivatives. Z=D In Oz dx ду

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Q: If xy^2 = 4 and dx/dt = -5, then what is dy/dt when x = 4 and y = 1?

A: To find dydt, when x =4 and y =1. Given information: xy2=4 and dxdt=-5 Formula used: 1.)…

Q: If y = 3x dx + 4x and dt 2, find when x = 4. dt dy dt

A: y=3x3+4xdxdt=2,

Q: If y=x² - 4x and x = √2r²+1; find dy dt when t = √2.

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Find the general solution of the DE: dx 6- dt2 + 12- - 8x = 0 %3D - dt3 dt

A: Given ODE is d3xdt3-6d2xdt2+12dxdt-8x=0

Q: Find dy/dt. y = tan x; dx/dt = 3, x =π/4

A: Consider the following function:        y=tanx finddydt when dxdt=3,x=π/4.

Q: Find both first partial derivatives. . z = ln x/ y

A: Given that z=lnxy

Q: 15 dy dt 2-

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Q: 5. x- + Px = sin t %3D dt

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Q: gin (t) et dt

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Q: ) Find: dx/dt  at  x=−4  if  y=−3x^2−2  and dy/dt=1. dx/dt=

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Q: 6. If x = y3 - y and dy/dt = 5, then what is dx/dt when y = 2?

A: The given equation are x=y3-y,dydt=5  and y=2.

Q: dx 5 x + 2y 2 dt dy 3 ーX 4 – 2y dt

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Q: Find both first partial derivatives. z = sinh(6x + 19y) dz дх dz ду

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Q: Find both first partial derivatives. z = 2y2√x

A: fx = differentiate with respect to xfy=differentiate with respect to yddxxn=n xn-1

Q: Compute the differential dy for y = 7x° – 4x2. dy =||

A:

Q: Let xy = 1 and dy/dt = 3. Find dx/dt when x = 1?

A: Consider a function u(x) such that, Now, according to chain rule,  The given information is,

Q: Find both first partial derivatives. z = sinh(4x + 8y) az ax az ay II

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Q: Solve the IVP dy/dt + 2(t + 1)y^2 = 0, y(0) = −1/8

A: To solve the IVP dy/dt +2(t+1)y²=0, y(0)=-1/8

Q: The time rate of change of liquid circulating in two tanks is govemed by dy -0.02x + 0.02y, = 0.02x…

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Q: Solve integration by (udv) T/2 DS Š X cos(x) dx 2) { X cos (ux) dx 7/2

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Q: Solve simultaneous equation dx/dt=2x+3y , dy/dt=x+4y , x=-3 , y=1

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Q: Suppose 4x + 9y - 25, where x and y are functions of t. (a) If dy/dt-, find dx/dt when x = 2 and y =…

A: Given: 4x2+9y2=25 Since, x and y are functions of t, therefore differentiating each sides with…

Q: Find both first partial derivatives. z = ln√xy

A: Given  z = ln√xy. We need to find both the first partial derivatives of the above function.

Q: If X+y = x-y x2. -y2 and dx/dt = 12, then what is dy/dt when x = 1 and y = 0? О 12 O -12 12

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Q: 3. dy/dt = e e- -∞ <yo <

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Q: Find both first partial derivatives. z = cosh xy2

A: Given: z=cosh xy2 To determine: ∂z∂x&amp; ∂z∂y

Q: d²x dx 5 dt2 2- 3x = -9t2 – 1 - - dt dx When t = 0, x = 1, = 0, find x when t = 2 dy %3D -

A: Please see the below picture for detailed solution.

Q: Assume that 2x + 3y = 12 and dy/dt = -2. Find dx/dt.

A: Assume,

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

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Q: If y = 2x³ +5 and dx = 3 then find dt dy when X = -2 dt

A: Given  y=2x3+5dxdt=3 To find dydt, when x=-2

Q: Find both first partial derivatives. z = x2e2y

A: Given function is z=x2e2y. Partial derivative means derivative of function with respect to one…

Q: THE IVP

A: Consider the provided differential equation with initial condition is,

Q: ди + 3x- = 1 + u, dx ди -co 0, dt u(x, 0) = f(x).

A:

Q: Find the first partial derivatives of the function. f(x, у) : cos(t5) dt fx(x, y) = fy(x, y) =

A: We use the leibniz derivative.