Show that : y' = 1 when y(x) = sin-(x) %3D V1– x2

Q: 3x4-4 cos x = -6

A: Find d2y/dx2 implicitly in terms of x and y3xy − 4 cos x = −6

Q: Find y" by implicit differentiation. x² + 5y2 = 5 %3D

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Q: Find y ' if sin (x+ y ) = y 2   cos x

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Q: If Sin-'x= Iny, show %3D ( l-xx) day - dx d X 2 x dy =y

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Q: Find dy/dx for x*+siny = x'y

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Q: Find of an

A: We are asked to find y'

Q: y = x * (sin 1x)² – 2x + 2v1-x² * (sin-1x), Find dy dx

A: Given that equation of y and we find dy/dx. We know that d(sin-1x)/dx = 1/√1-x2. And d(xn)/dx =…

Q: dy for the following functions : dx 1. Find 3(x – 1) (ans.: 5) Sec² /2x +7 15) y=\tan /2x +7 (ans.:…

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Q: 2- Solution of the following function {(dy/dx)-(cotx) y=(csc x)y³ }

A: The differential equation is given as dydx-(cot x)y = (csc x)y31y3dydx-1y2cot x = csc x…

Q: Solve the DE by eliminating the arbitrary constant of x sin y + (x^2)y = C

A: Given that the expression xsiny+x2y=C. Differentiate with respect to x.…

Q: 7. Find y' for y = (sinx)*.

A: The given function is y=(sin x)x. Rewrite the given function as follows.

Q: 18. y = sin x cos x

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Q: 21, e = x - y x/) find dy/dx by implicit differentiation

A: The objective is to find dydx of the function exy=x-y by implicit differentiation.

Q: Find y' if y = sin² (5+7)

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Q: sin If y = show that (1- x²) 1-x -1 x. d'y -3x dy drソミ0 dx? ーy=

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Q: y = In (3²×) + sec (Inx²) + tan¬1(In5x)

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Q: dy for y = 4 sin (x²). dx ] B2 (c): Find %3D

A: Need to fin dy/dx

Q: 13. (D -1)y = x' sin 3.x

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Q: (3– 3cos5x)} (3x² +2x-7)² (e - sinx +3x) y= Find dy/dx if

A: That's computational, take a careful look.

Q: y'' + 4y' = sin^2 x

A: Given differential equation is: y''+4y'=sin2x Solution of differential equation is sum of…

Q: Find d²y/dx² if y = =x cos(3x) — sin²(x). -

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Q: Solve: y" + y'tanx = (y')²

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Q: 11. y = tan e³x + etan3x

A: We can find y' as below.