d’y d²y D. = 3e* +4x2 dx dx2

Q: What is dy/dx of 1/2e^2x

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Q: х2+1 dy 4) хеУ dy- *dx 5) х?у 3 (1 + х)Csc y y dx 6) хеУ dy + (*+1) dx =0 y

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Q: Calculate dy/dx using implicit differentiation. 3x + 4y3 = 7

A: 3x + 4y3 = 7 We need to find the derivative using implicit differentiation.

Q: 2. dy dx

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Q: tan20 sec2ede In 2 edx 3. 1. (a² + a²tan²0)² 2ex- 1 x'dx dx x- 1 2. 4. (1+ x2)3

A: As per our policy, only the first three subdivisions will be solved. For the remaining subdivision,…

Q: dy Let ry = 1 and dt 5. dx when x = 5. dt Find

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Q: 5y + sin y = x²

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Q: Differentiate implicitly to find dx Зху + 5 3 0 dy %3D dx

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Q: Find dy/dx, where xsiny +ysinx=1.

A: Given - xsiny+ysinx=1 To find dydx Here we will use the following formulas- ddx(uv)=udvdx+vdudx…

Q: Find dy ду é^sinx in sx

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Q: tanx dx = -In/secx|+C^O .BO In|secx|+CO In/cscx| +CO -In|cscx|+C°O .D

A: We need to evaluate the following integral I = ∫tanxdx

Q: = vt – 2, d²y t – 2. d²y y = t² – 3' dx2

A: x=t-2y=t2-3

Q: Bind dy, 4. Ssinx.cosx sinx-coSX 1 +2.Ln X

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Q: = sin(5x) for y(0) = 2

A: the solution is, y = (11 - cos5x)/5  The detailed solution is as follows below:

Q: Approximate - -1x+3 -dx using trapezoidal rule with n=4 and Simpson's rule with n=4.

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Q: Differentiate implicitly to find dy/dx. ²+ y² - y² = 29 dy dx 11

A: This question is based on implicit differentiation.

Q: Jz{sinh³ 4z*)'^ ² - dz 1/4 cosh³ 4z'

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Q: find dy / dx by implicit differentiation.

A: Given equation is x4y-8xy+3xy2=9. To find dydx. Solution: Power rule of differentiation states that:…

Q: 30. 5e dx 31. Зи du - 1 33. x² dx 35. (x+5)* 37. xp (3 In z + 2)4 39, -dz

A: We will solve the integration.

Q: Use Leibniz's rule to find dy dx dy dx for y= 8x-1 √ (t4-5) dt.

A: Concept: Newton Leibniz Theorem : Newton Leibniz A formula for differentiating a definite integral…

Q: Find dy/dx if 5x1/2 + 6y1/2 =15. dy/dx=?

A: We have to find dydx for 5x12+6y12=15.

Q: 7) y = exz 8) y = 3 x ²

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Q: (a) --y = 2x?y, y(1) = 1 dy dx

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Q: (continue solution of de) (2ysinxcosx - y + 2y²e*Y" )dx = (x - sin²x - 4xye*y" )dy

A: Using method of exact differential equation.

Q: dx Q2. Integrate

A: Given,I=∫1x2+15dx Consider x=tanu and u=arctan(x) then, dx=sec2udu…

Q: 3. у?dx— x(2х + Зу)dy %3D -

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Q: (3 sin y – 5x)dx + 2x2 cot y dy = 0 -

A: Solution :-

Q: Find dy/dx when y=√x^2-x

A: y=x2-x

Q: ] Integrate by parts to show that Vx dx = 2e4 - e* dx. ex. е —

A: To evaluate the given integral choose  √x as the first function and ex as the second function and…

Q: dy Exc:" of y = tanh (x5 – 5x)² --

A: Solution:Given         y=tanh4(x5-5x)2  To find dydxFormula:ddx(xn)=nxn-1ddx(tanh x)=sech2x

Q: Evaluate dy/dx at x=2 and y=3  if   x4 +  y4 =16.

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Q: 2. [ y dy dx carctan3/2 3 secx 3/2

A: Topic  = Integration

Q: ex dx

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Q: Differentiate implicitly to find dx 2y? - xy + 3x = 4 dy dx

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Q: Differentiate. In x y = dy dx

A: The quotient rule of differentiation is, ddxfxgx=gxddxfx-fxddxgxgx2. we have the differentiation…

Q: Find dy/dx by implicit differentiation. 7x?y + 4y²x = -5 dy/dx

A: Given that 7x2y+4y2x=-5       ...(1)

Q: dy dx 118 (x = 3x - 5

A: Topic:- differential equations

Q: dy Use an appropriate technique to find dx from x² + y² = (2x² + 2y² -x)*.

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Q: Find the geneul suluticn dy t. + 2y= 2X 2. dx

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Q: dy Differentiate implicitly to find dx exy 2x+9y+3

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Q: dy Differentiate implicitly to find dx 5. 3 4 x'y +8x -3y +2 dy 口 dx

A: Given query is to find the derivative of the function using implicit differentiation.

Q: (у-sinx) dy + dx = 0.

A: dy+(y-sinx)xdx=0⇒(y-sinx)xdx=-dy⇒(y-sinx)dx =-xdy⇒ydx-sinx dx =-xdy⇒ydx +xdy = sinx dx⇒d(x·y) = sinx…

Q: Differentiate the function. 1 y3= (2x +3) dy dx

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Q: dy sin: 8. x +2y = dx y(2) = 1

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Q: 4) dy dy dz 5) dy dy

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Q: Find dy/dx by implicit differentiation. 2x2 - 2y? = dy/dx =

A: We can get dy/dx by differentiating both sides w.r.t x. The solution is explained in step 2.

Q: Cosx 2) ). y dx+ týž - Sinx (²) dy = уч

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Q: 9. 2y(у? — х)dy — dx, when x %3D2,у %3D 2

A: Given that: 9.     2y(y2-x)dy=dx,    when x=2, y=2     NOTE: As per our answering guidelines, we can…