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If y=x^x ,fin d(d^2y)/(dx^2)...

If `y=x^x ,fin d(d^2y)/(dx^2)`

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We have,
`y=x^x`
On taking logarithm both sides, we get
`lny=ln(x^x) ............(1)`
`lny=xlnx`
...
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RD SHARMA-HIGHER ORDER DERIVATIVES-Solved Examples And Exercises
  1. If x^m y^n=(x+y)^(m+n), prove that (d^2y)/(dx^2)=0

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  2. 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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  3. If y=x^x ,fin d(d^2y)/(dx^2)

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

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

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

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

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  8. If y=(log)e(x/a)^x ,then x^3y2=

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  9. If sin^(-1) (1 – x) – 2sin^(-1) x = π / 2,then x is equal to

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

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

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  12. If x y-(log)e y=1 satisfies the equation x(y y2+y1 2)-y2+lambday y1=0,...

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  13. If x=f(t )cost-f^(prime)(t)sinta n dy=f(t)sint+f^(prime)(t)cost ,t h ...

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  14. If x=f(t) and y=g(t), then (d^2y)/(dx^2) is equal to

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  15. Let f(x) be a polynomial.Then, the second order derivative of f(e^x) ...

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  16. If y=tan^-1((log(e/x^2))/(log(ex^2)))+tan^-1((3+2logx)/(1-6logx)), the...

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  17. If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)fx-xy(x)= 1 (b) -1...

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  18. If f(x)=(cosx+isinx)(cos2x+isin2x)(cos3x+isin3x)......(cosn x+isinn x)...

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  19. (d^(20))/(dx^(20))(2cosxcos3x)is equal to (a)2^(20)(cos2x-2^(20)cos3x...

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  20. If x=acosn t-bsinn t ,t h e n(d^2x)/(dt^2) is n^2x (b) -n^2x (c) -n ...

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