d Using the Chain Rule Twice Calculate 1+ Vx2 + 1. dx

Q: Q5. Use variation of parameters to solve the nonhomogeneous ODE. y" + 16y = sec³4x

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Q: Xtan+4]dx - xdy= of + y]dx - xdy=0

A: Given differential equation is xtanyx+ydx-xdy=0 This equation can be rewritten as,…

Q: dx 3. If 8c²xy = (x² - y2)2, find- dy

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: V2 Evaluate the integral dx. Va2 +1

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Q: Let y3 - 4x = 2xy. Find d2y/dx2. Show work please.

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Q: 4x + 5 6 - Evaluate the integral dx. V3 – a? a)5 arcsin V3x + 4/3 – a2 + C b)5 arcsin V3x – 4/3 – x2…

A: =?

Q: Q5) Use the Chain Rule to express dy /dx in terms of x and y: y = csc t and x = sec-1t

A: To find: The value of dydx in terms of x and y. Given information: y=csct,x=sec-1t

Q: 1. S(3 – 2x – x*) dx

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Q: Sv-4 - y-3) dy

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Q: (d) Evaluate [(2xr² – 3x)dxusing formula develop in part (c)

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Q: Find dx. Using the substitution u=3 – 2x (3— 2л)5 |

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Q: dx using miscellaneous substitution will yield to secx + 1 nsforming - S 1+2 / dz √²-22² dz 1+z²…

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Q: 18 Find J4 dx.

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Q: Q2\ find when y = dx x²-1

A: y=xx2-1⇒y=x12x2-1⇒y=x1212x2-1⇒y=x14x2-1

Q: Q2: Find the integration by applying substitution method: 7 dX (X - 1)VX- 2x - 48

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Q: Transforming A S B © D dx secx + 1 7 dz 1-2² 1==323d² -dz 1+z² [1+2²21 2-272 1+z² -dz -dz using…

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Q: B. Integrate the following using the basic rules of integration and substitution. 1. fx2 +5x-x-3 dx…

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Q: e dx 1- e2x (integration by substiution)

A: NOTE: Refresh your page if you can't see any equations. . ...............(1)

Q: Q2: EVALUATE * S I5(x) dx Js(x)

A: To find : ∫J5xdx Using the formula  ∫Jn+1xdx=∫Jn-1xdx-2Jnx Here n=4

Q: dx 3.J Jx2+16

A: Answered no. 3 We can solve the given problem using the concept of integral trigonometric…

Q: 2 4) d?y |1+ () dx2 dx, Find the: Туре: Order: Linearity: Why?: Unknown Function: Independent…

A: Topic:- differential equations

Q: 8. Find when x = t3 -t and y = 4 –- t². dx'

A: Here, the given functions are: x=t3-t & y=4-t2⇒x'(t)=ddt(t3-t)=ddt(t3)-ddt(t)=3t2-1…

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 dy さ× when 3In X リ=(メ+z)m

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Q: 2. t23* dt

A: The given problem is solved below in detail.

Q: Using the Chain Rule Find dy/dx for y = (x2 + 1)3

A: Given, y=x2+13 We can write given function as, y=x2+12x2+1 Now by using the chain rule,

Q: Use the chain rule to show that for a>0, x>0, d/dx xa = axa-1

A: We know that,The derivative of a function f(x)=xn usingpower rule is given asf'(xn)=nv(n-1), n>0…

Q: dx 10. J V2x2-1

A: See the details solution in below

Q: 94. Find dy/dx if y - 2 by using the Chain Rule with y as a com- position of a. y- u' and - V b. y -…

A: a) Given y=x32 The chain rule state that dydx=dydu·dudx

Q: Using integrating factor, solve  dy/dx - 3y = 6

A: To find the solution of the differential equation.

Q: dx using miscellaneous substitution will yield to secx + 1 Transforming S Ⓒ √ ²² +²2 dz (Α) -z²…

A: This question can be solved by substituting z=tanx2

Q: a2z If z = In(x² + y²), find a²z + dx2 ду?

A: Given, z=lnx2+y2

Q: b) y = [ dx Integrate. 13 +5

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Q: 4x -dx using Trapezoidal Rule with n=5 x2 + 4 Evaluate

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Q: dx 62 + x² Integrate:

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Q: dy for all of : dx Find 3 |x(х-2) 1- y = xvlnx 2- у 3 х2+1

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Q: Q2: Find the integration by applying substitution method: 7 dX (X – 1)VX2 – 2x - 48

A: Given,             ∫7x-1x2-2x-48dx

Q: t of integration.) dx 5 + v2x

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Q: Use the chain rule to find dy/dx for th following (a) y= (3x^2 - 13)^3

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Q: Evaluate [(x² +2) dx , using Trapezoidal rule, by taking N = 8.

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Q: dy Find for x=secy dx A xsinx B D 1-x?

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Q: Find the antiderivate of dx/(x2+4)3/2

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Q: Integrate dx/a^2+(x+b)^2

A: Take the substitution that x+b=t.

Q: dy Q5/ Find by using chain rule dx

A: Here, y = √( t2 - 5) + t x = t×√(4t + 8) + 7 dy/dx = (dy/dt) / (dx/ dt)

Q: Using integrating factor, solve dy/dx + 4/x . y = x

A: topic. - differential equations