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Find the 2nd derivative if x^3 log x wit...

Find the 2nd derivative if `x^3` log x with respect to x.

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The correct Answer is:
`x(5+6logx)`
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NAGEEN PRAKASHAN-Continuity and Differentiability-Exercies 5l
  1. Find the 2nd derivative if x^3 log x with respect to x.

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  2. If y=tan^(-1)x^3 then find (d^2y)/(dx^(2)).

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  3. Find the 2nd dervative of e^(ax+b) with respect to x.

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  4. If y=x+cotx then prove that sin^2x(d^2y)/(dx^2)-2y2x=0.

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

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

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  7. (i) If y=asin(log x) then prove that x^(2)*(d^2y)/(dx^2)+x(dy)/(dx)+y=...

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  8. If y=(sin^(-1)x)^2 then prove that (1-x^(2))(d^2y)/(dx^2)-x(dy)/(dx)-2...

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  9. If y=sin(sinx) then prove that (d^2y)/(dx^2)+tanx. (dy)/(dx)+y cos^2...

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  10. IF y=e^(tan^(-1)x) then prove that : (1-x^(2))(d^2y)/(dx^2)+(2x-1)(d...

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  11. If y^3-3ax^2+x^3=0, then prove that (d^2y)/(dx^2)+(2a^2x^2)/(y^5) = 0

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  12. If y=(t a n^(-1)\ x^2) , show that (x^2+1)^2(d^2\ y)/(dx^2)+2x(x^2+1)(...

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  13. If y=e^tanx then prove that: cos^2x(d^2y)/(dx^2)-(1+sin2x)(dy)/dx=0

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  14. If y=A e^(-k t)cos(p t+c), then prove that (d^2y)/(dt^2)+2k(dy)/(dx)+n...

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  15. If x=at^2,y=2 at then find (d^2y)/(dx^2).

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  16. If x=a(t-sint), y=a(1-cost) then find (d^2y)/(dx^2).

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  17. If x=sint" and "y=sin mt" then prove that "sqrt(1-x^2)(d^2y)/(dx^2)-xd...

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  18. If y=(sin^(-1)x)^2+(cos^(-1)x)^2, then prove that (1-x^2)y2-xy(1)-4=0.

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