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If y=log(sinx),"p r o v et h a t"(d^3)...

If `y=log(sinx),"p r o v et h a t"(d^3)/(dx^3)=2cosxcos e c^3xdot`

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If y=log(sinx) , prove that (d^3y)/(dx^3)=2cosx cos e c^3x .

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RD SHARMA ENGLISH-HIGHER ORDER DERIVATIVES-All Questions
  1. If y=x+tan x, show that cos^2 x (d^2y)/(dx^2)-2y+2x=0

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  2. If y=e^-x cos x, show that (d^2y)/(dx^2)= 2e^-x sin x

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  3. If y=log(sinx),"p r o v et h a t"(d^3)/(dx^3)=2cosxcos e c^3xdot

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  4. If y=x^3logx ,"prove that"(d^4y)/(dx^4)=6/xdot

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  5. If y=(logx)/x ,show\ tha t(d^2y)/(dx^2)=(2logx-3)/(x^3)

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  6. If y=2 sin x+3cos x, show that (d^2y)/(dx^2)+y=0

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  7. Find . (d^2y)/(dx^2),ifx=a t^2,y=2a t.

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  8. If x=sin theta,y=cosptheta,p rov e \ t h a t (1-x^2)y2-x y1+p^2y=0,w ...

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  9. If y=tan^-1x find (d^2y)/(dx^2) in terms of y alone.

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  10. If x^m y^n=(x+y)^(m+n), prove that (d^2y)/(dx^2)=0

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  11. If y^3-y=2x ,p rov et h a t(d^2y)/(dx^2)=(-24 y)/((3y^2-1)^3)

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  12. If y=x^x ,f i n d \ (d^2y)/(dx^2)

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  13. If y=sin^(-1)x , \ s how \ t h a t \ (d^2y)/(dx^2)=x/((1-x^2)^(3/2))

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  14. If y=Acosn x+Bsinn x ,s howt h a t (d^2y)/(dx^2)+n^2y=0

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  15. If y=tanx+secx ,p rov e \ t h a t \ (d^2y)/(dx^2)=(cosx)/((1-sinx)^2)

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  16. If y=(a x+b)/(x^2+c), then (2x y1+y) y3=

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  17. If y=(log)e(x/a)^x ,then x^3y2= (a) (xy1-y)^2 (b) ((y-x y1)/(y1))^2 ...

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  18. If sin^-1x + sin^-1(1-x) = sin^-1sqrt[1-x^2],then x is equal to

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  19. If y=2/(sqrt(a^2-b^2))tan^(-1){sqrt((a-b)/(a+b))tan(x/2)} , then show ...

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  20. If y=x^(n-1)lnx then x^2y2+(3-2n)x y1 is equal to (a) -(n-1)^2y (b) (...

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