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Let f(x) be a polynomial.Then, the seco...

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

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Let `y = f(e^x)`
`dy/dx = f’(e^x) e^x`
`(d^2y)/(dx^2 )= f’’(e^x) e^x e^x + f’(e^x) e^x`
`= f’’(e^x) e^2x + f’(e^x) e^x `
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RD SHARMA-HIGHER ORDER DERIVATIVES-Solved Examples And Exercises
  1. If x=f(t )cost-f^(prime)(t)sinta n dy=f(t)sint+f^(prime)(t)cost ,t h ...

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

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

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

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

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

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  8. 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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  9. In (dy)/(dx),x is a independent variable and y is the dependent vari...

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  10. If y^2=a^2cos^2x+b^2sin^2x then prove that (d^2y)/(dx^2)+y=(a^2b^2)/(y...

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  11. If y=sin^(-1)x , show that (d^2y)/(dx^2)=x/((1-x^2)^(3//2))

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  12. If y=Acosn x+Bsinn x , show that (d^2y)/(dx^2)+n^2\ y=0 .

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  13. If y=A e^(m x)+B e^(n x) , show that (d^2y)/(dx^2)-(m+n)(dy)/(dx)+m n ...

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  14. If y=Acos(logx)+\ Bsin(logx) , prove that x^2\ (d^2y)/(dx^2)+x(dy)/(dx...

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  15. If y=tanx+secx , prove that (d^2y)/(dx^2)=(cosx)/((1-sinx)^2)

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  16. If y=tanx , prove that y2=2y y1 .

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

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

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  19. If y^3-y=2x , prove that (d^2y)/(dx^2)=-(24 y)/((3y^2-1)^3) .

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  20. If e^y(x+1)=1 . Show that (d^2y)/(dx^2)=((dy)/(dx))^2

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