-n If y=a(x+ Vx* +1) +b(x - -1)" prove that .2 (x²–1) d'y dy n°y =0. dx dx

Q: Graph the curves y = x1/3(x - 4)

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Q: d'y dy -4- 4- dx? dx -3y=0. y(0)=1, y(0)=5

A: According to the given information, it is required to solve the given differential equation.

Q: Find d²y/dx². y=xsin x 10 cos x

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Q: dy Prove that dx of x2 +2x is f'(x)=2x + 2

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Q: 을(22 + y7) %3D (25) d. da da d 을 (2) + 옮 (v?) 3D0 d dæ da a function of x and using the Chain Rule,…

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Q: dy -1, then -2x If y= csc-(e")+Ve-1. then - Select one: -2 e+1 e2x. -1 e-1 2-1 -1

A: Given, y = csc-1ex + e2x-1  We have to find dydx.

Q: Solve: dy/dx = 1+e(y-x+5) Show all the work!!

A: Step 1: SolutionGiven differential equation: dxdy​=1+ey−x+5We have to solve the given differential…

Q: x+y y² +1 #2) (x + tany)dx +- -dy = 0.

A: here we have to solve the differential equation.

Q: Consider y=(x2+1)2x a) find dy/dx b)Evaluate y'(1)

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Q: (x2+1) dx = 0. xe'dy + dx 3 0. y

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

Q: dy 1-x Find given that y = x'-* dx

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Q: b) y = In(xeVx + 2)

A: The solution are next step..

Q: (a) S₁ 2 x² - 2x dx (0) 1/2₂ dx (c) .f x¹ ln x dx, n ‡ −1

A: (a) Here, we have given an integral, I=∫122x2-2xdx. To integrate ∫122x(x-2)dx, we can use…

Q: If y - y = 2x, then prove that 2 ence, show that x² - 1\d²y dx² 27 + X. dx² 1 dy dx = (3y² - 1)³

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Q: and d^2y/dx^2 for

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Q: y = (e¯2 +1)(x +1) a) Find Cari dy i) dx d²y ii)- dx?

A: We need to find :

Q: Find the derivative of the function: O f(x) 0 17 16 0-17 4 17 4 O-17 16 2x - 7 3x - 2 at x = 2

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Q: Find dy/dx: b) y = x² (x – 1)³

A: We have given y=x2x-13. To find: dydx. Solution: Power rule of differentiation states that:…