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If y (k) is the kth derivative of y with...

If `y _(k)` is the kth derivative of y with respect to `x,y= cos (sin x) ` then `y _(1) sin x + y_(2) cos x =`

A

`y sin ^(3) x`

B

` - y sin ^(3) x`

C

`y cos ^(3) x`

D

` -y cos ^(3) x `

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The correct Answer is:
D
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DIPTI PUBLICATION ( AP EAMET)-DIFFERENTIATION -EXERCISE 1D
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  2. If y= sin (sin x) then y (2) + (tan x) y (1) + y (cos ^(2) x)=

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  3. If y (k) is the kth derivative of y with respect to x,y= cos (sin x) ...

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  4. If y = ax ^(2) + b// x then x ^(2) y (2) =

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  5. If y = ax ^(4) + (b)/(x ^(3)), then (d ^(2) y)/( dx ^(2)) =

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  6. If y = a cos x + (b + 2x ) sin x then y (2) + y =

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  7. If y =a + be ^(-4x) then y (2) + 4y (1) =

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  8. If y = ax + b//x then x ^(2) y(2) + xy (1) -y=

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  9. If xy = ae ^(x) + be^(-x) then xy (2) + 2y (1) - xy =

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  10. If y = (x+ sqrt(x ^(2) -1))^(m) then (x ^(2) -1) y(2) + xy (1)=

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  11. If y = xe ^(- 1//x) then x ^(3) y (2) - xy (1) +y=

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  12. If y = e ^(Sin^(-1)x ) then (1 - x ^(2)) y (2) - xy(1) -y=

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  13. If y = sin (log (e) x) then (x ^(2) (d ^(2) y)/(dx ^(2)) +x (dy )/(dx)...

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  14. If y =a cos (log x) + b sin (log x) then x ^(2) y (2) + xy (1)+y=

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  15. Cos^(-1) ((y)/(b)) =2 log "" ((x)/(2)) , x gt 0 implies x ^(2) (a ^(2)...

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  16. If y sqrt(1+ x ^(2)) = log ( x + sqrt( 1 + x ^(2))) then (1 + x ^(2))...

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  17. If y = ae ^(-bx) cos (cx +d) then y (2) + 2by(1) + (b ^(2) +c ^(2)) y...

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  18. If y = ax ^(n+1)+ bx ^(-n) then x ^(2) y (2) =

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  19. If y = ae ^(nx) + be ^(-nx) then y (2)=

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  20. If y = e ^(-kx //2) (a cos nx + b sin nx) then y (2)+ky(1)+ (n^(2) + k...

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