Show that if y = ex² dy cosh x then y(2x + tanh x) %3D dx Differentiate with resnert to y 1.

Q: xe 2, x Cosz dx

A: Integration by parts, ∫udv=uv-∫vdu u is the first function Given integral, ∫x exdx

Q: Find the dervative: -1 y = sinh 2 dy dx

A: I have stated the used formulas in the solution

Q: `s): The area of the surface obtained by rotating the curve y = ln(3x - 2), for 3 ≤ x ≤ e², about…

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Q: Find the implicit deriviate (dy/dx) of (2x+3y)1/3=x2

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Q: Find dy/dx by implicit differentiation. sin x + cos Y= sin x cos Y dy/dx

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Q: Evaluate the double integral : (y³ – 12x) dx dy -

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Q: dy/dx if y = cosh 2 Jx +1 2 JX +1

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Q: If y=sin-1x then dy/dx= 1/dx/dy for all x in [-1,1] True or False.

A: Given statement If y=sin-1x then dy/dx= 1/dx/dy for all x in [-1,1] is false.

Q: Find dy/dx by implicit differentiation. tan(x – y) 1+ x2 dy dx ||

A: Given

Q: If flix.y)=XSin²(y)+y°Cos(x) prove that fn=2[Costy).Sin(y) ySin(x)]

A: First of all, we partially differentiate function f wrt. x and then we partially differentiate the…

Q: Ho Find (dy/dx) for: tanh-¹(x y) + e(x+y) 5 cos(y)

A: It is given that, tanh-1xy+ex+y=5cosy. The objective is to find dydx. Formulas used:…

Q: 2. Find the value of dx at y=2 if x=z²+5z and z= (y² + 2y)²/3.

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Q: 2. Z dx dy dz to

A: (5) Given integral is ∫02∫04−z2∫02−zzdxdydz.…

Q: Evaluate the double integral: sin(y) /y³ dy dx.

A: Change the order of integration to simplify the integral .               Disclaimer: Since you have…

Q: Particular integral of dy +3 dx dy + 2y = e-2a + sin is dx?

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Q: Find dy/dx by implicit differentiation. tan(x – y) 1+ x2 dy dx

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Q: Find dy dx 21) tan y = eX + In 4x eX + 4 A) - sin² y хeх + 4 B) - xcot y

A: Given;  tany=ex+ln(4x).

Q: Differentiate. In x y= 11 y3D dx

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Q: Use the Euler method with dx = 0.2 to estimate y(2) if y' = y/x and y(1) = 2.  What is the exact…

A: Given: dx=0.2 y'=yx and y(1)=2

Q: Figure out these antiderivatives. S dx /1-х2 arctan(x) dx 1+x? ( In(x))* dx 2x

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Q: Find dy. y = 5 In (5+ x°) dy =

A: If you like the solution then please give it a thumbs up.... The Answer is:           Result :…

Q: S tan ax secex dx 3

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Q: dy 1- cosh x + (sinh x)y = e¯x dx 2 dy 2- - y = e*/2y³ dx

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Q: Find dy/dx by implicit differentiation. x²y2 + x sin(y) = 4 dy/dx %3D

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Q: ■ Find dy /dx  by implicit differentiation ycos x = 1+ sin (xy )

A: The given equation is ycos x=1+sinxy.

Q: Show that u (X ) = 3X+ 2x is asolution to the integral equation 3(1+x)? X - S sinh (x-t) ultJ dt

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Q: Find dy/dx by implicit differentiation. eX/y = 3x – y y' =

A: Differentiate wrt x

Q: dy In(5x + 5) Find for y = - dx 3e2x dy dx

A: Given, y=ln(5x+5)3e2x

Q: e following integral: 23 8xyz dz dx dy. 120

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Q: IF x = asec'0 and y = atan '0 dy Find at 0 dx 3

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Q: Find the general and particular soulution of dy/dx=3y, where y=6 and x=0

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Q: B. Verify that dz/dy dz/dx 1 =. If xy + z = sinz.

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Q: 3. Find dy/dx of: x(x-y)-xーy evaluated at x = 0.001 and y = 0.002

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Q: (g) y = Vtanh 3r (h) y= sinh(cosh 2.x)

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Q: Find dy/dxdy/dx by implicit differentiation. 2cos(x)sin(2y)=−4

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Q: Find dy/dx by implicit differentiation. tan(x − y) = y / (3 + x^2)

A: I have stated the used formulas in the solution.

Q: If x = t- sin t and y = 1- cost dy find the dx

A: Given, x=t-sinty=1-cost       Find: dydx

Q: Find dy/dx.   e4x=sin(x+3y) dy/dx=

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Q: 2. Evaluate dy/dx for y= x In x 1+inx

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Q: dy = 3; find dt dx when x = 2. dt Related Rates: Given y = x³ – 2x and

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Q: Find dy/dx by implicit differentiation. xy = 8x + 9y2   dy/dx= ?

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Q: sinh x – 1 dx cosh x

A: The given integral,        ∫sinhx-1coshxdx

Q: Find dy/dx by implicit differentiation. sin x + cos Y = sin x cos Y dy/dx =

A: Given- sinx+cosy=sinxcosy To Find- The value of dydx by implict differentiation. Concept Used- The…

Q: dy 1- cosh x+ (sinh x)y = e¬* dx

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

Q: 7. Given y = sinh(e* +tan (2x)-cos (x+1). Consider | dy (i) et 1 dx 1+e2x 1+4x 1-(x+1) dy (ii) ex 1…

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you…

Q: dy Find in terms of x and y if x In y + yo = 4 ln x. dx

A: Solution is written in below steps.

Q: 12. Differentiate.   y=4/2−7x dy/dx=nothing   Enter your answer in the answer box.

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Q: 3) [ - cos dydx X X In 8 In y 4) S S e**y dxdy

A: (3) we have to evaluate ∫π2π∫0x21xcosyxdydx let  u =yx ⇒dudy=ddyyx         =1xddyy=1x⇒du = 1xdy…

Q: Find dy/dx by implicit differentiation. VTy = x'y +33 dy/dx =

A: The given equation is xy=x7y+33.

Q: .2 dy Find for y dx V6 – x5 - dy %3D dx

A: We have to find dydx

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.