Given that y = 7 ln u and u = 6x? dy Use the formula dx dy in terms of x. dx dy du to find dz du

Q: Given x 19 In(t) and Y 361 t2 then find dy dx dy dx?

A: To find: The value of dydx and d2ydx2. Given: The values are x=19 ln t and y=361t2. Formula used:…

Q: Find the particular solution of y (1+2 In?2) dx + xdy = 0 y(e) = e.

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Q: Given x = 2 cost + 10 and y= 8 sin? t dx (i) dt dy (ii) dt dy (iii) dx

A: Let's find.

Q: If x? + y? = 100 and dy 8, find dt dx when y = 6. (Enter your answers as a comma-separated list.) dt…

A: Given that x2+y2=100dydt=8To find :dxdt when y=6Solution:x2+y2=100x=100-62=8x2+y2=100Diffranciate…

Q: dy dx\, Given that x = t e and y = 1² e“ +1¸ Find = - 1

A: We have to find derivative at that point

Q: Find the general solution of dy + y cot(x) = 6 csc'(x). dx

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Q: Given a = 2 cost + 17 and y = 3 sin? t dx dt dy dt dy dx

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Q: Given x = 2 cost + 17 and y = 3 sin? t dx dt dy dt

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Q: Given e = 98 sint + 24 and y = 98 cost +3 da (*) dt dy (é) dt dy (é) da ||

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Q: dy dy implicitly in terms of x and y. Hence, find d.x Given sin(xy) + 3e 3y?. Find dx when x = 0 and…

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Q: Use Euler's modified formula to find an approximate value of y whenx = 0.3, given that = x+y and…

A: Given  dy/dx = x+y and y(0)=1 To determine y(0.3) using Euler's modified formula

Q: dy = y? – 4 dx

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Q: Given x = 4 In(t) and y = 16 t² then find dy dx d²y dx?

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Q: Given x = 5t – 27 and y= 25 sin t dy (i) dx d'y (ii) dx? ||

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Q: Find the values of a and b that make following D. E is exact (-) dx + (xy + 1) dy =

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Q: e) tan 5y – y sin r+3ry? = 9.

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Q: Given x 13 In(t) and y = 169 t² then find dy dx

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Q: d'y Find dx? given that 5xy = 25. Oa. O a. dy 2y 2 dx2 Ob. d'y 2y x2 Oc. d'y ,2 dx? O d. dy dx?

A: Topic:- Derivative Correct option = b

Q: dx x- y- dy dx (Separation of variable) dy

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Q: Given z = 2 cost +3 and y= 3 sin? t dx dt dy dt dy dx

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Q: dy = ( e )dx

A: See the attachment

Q: √ay-x² So Sie So dz dy dx

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Q: Answer the given DE below: x (dy/dx) +y=y^2

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Q: Given x = 6 ln(t) and y = 36 t² then find dy dx dx?

A: Let x = 6 ln(t) and y=36t2 Differentiate x with respect to t dxdt=ddt6 ln(t)=6ddtln(t)=6·1tdxdt=6t…

Q: 2xy dx + (x2 – 1)dy = 0 %3D

A: This question is related to differential equation from calculas . We solve this problem using…

Q: b) Find fo dy for y = Vt-1 t = sec?x sint

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Q: Find the general solution dy y cos a + 3xy %3D dx

A: We solve the given differential equation by separation of variables.

Q: Find a solution to the SDE dX; = X,(ydX; + tdt), where y ER is a constant and Xo = 1.

A: The given equation is dXt=XtγdXt+tdt. The given initial condition is X0=1. The integration formula…

Q: Given x = 75 sint + 30 and y= 75 cost +4 dx (i) dt dy (ii) dt dy (iii) dx || ||

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Q: Given x = 2 cost + 35 and y = 8 sin? t dx dt dy dt dy dæ || ||

A: Given equation is, x=2cost+35y=8sin2t

Q: A شعبة Given x2 + y? + z? = sin (yz) find dz/dx %3D

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Q: Given y = xy2 + e* calculate and report the value of dy when y = x = 1. dx

A: Differentiating using product rule

Q: Find for dy dæ² y(x) = cot(x) *= csc? dy dx? 2

A: Given query is to find the double derivative of cotx.

Q: Solve the first order o.d.e dy/dx=(1+y^2)e^x

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Q: Given that x = e'Iny, y > 0 dx (a) Using the product rule find an expression for dy dy and hence…

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Q: Solve the Following D.E x*dy = (z xy-j') dx %3D

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Q: e'dx+ cosx dy 2. t.

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Q: Given yz = ln(x+ z), find dz and dz fie

A: As we know that; The Power law; ddxxn=nxn-1 The Chain rule; fgx'=f'gx·g'x And c·f'=c·f' ; where c is…

Q: Approximate dx , using the open Newton-Cotes formula 4h Iscx)dx=125(x,)-S(x, )+2f(x,)]. 3

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Q: Given r = 15 In(t) and y= 225 t then find dy dx d'y da?

A: Given that x=15lnty=225t2

Q: Given a = 12 ln(t) and y = 144 t2 then find %3D dy dz &y dz2

A: x=12ln(t)y=144t2

Q: 7. x(3xy - 4y + 6) dx + (x-6x?y?-1) dy = 0.

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Q: Given x = 2 cost + 38 and y = 5 sin?t dx (i) dt dy (éi) dt (tt) dy (iii) dx ||

A: We can find the answer as below.

Q: Using dy = 3 dx and dx = 0.03, what is dy when x = 2? 2V3X – 2 dy = i (Write as an exact decimal.)

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Q: Given y is the square root of x. Find dx/dt when y=2 and dy/dt= 1.75

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Q: 10. Given that y = at x = 1. e* X + 1 Find, in terms of e, the values of . 최 and dx dx²

A: (10). Given: y=exx+1   As we know that; The Power law; ddxxn=nxn-1 The Quotient rule;…

Q: Given I = 4 In(t) and y= 16 t then find dy dx dy da?

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Q: Given a = 2 cost + 30 and y = 5 sin? t dx dt dy dt dy da || ||

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