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

If `y=e^(-x)cosx,` show that `(d^(2)y)/(dx^(2))=2e^(-x)sinx.`

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RS AGGARWAL-DIFFERENTIATION-Exercise 10I
  1. If y=2sinx+3cosx ,show that (d^2y)/(dx^2)+y=0

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  2. If y=a cos (logx)+b sin (logx), prove that x^(2)y(2)+xy(1)+y=0.

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  3. If y=e^(-x)cosx, show that (d^(2)y)/(dx^(2))=2e^(-x)sinx.

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  4. If y=sec x-tanx,show that (cosx)(d^(2)y)/(dx^(2))=y^(2).

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  5. If y=("cosec "x+cotx), prove that (sinx)(d^(2)y)/(dx^(2))-y^(2)=0.

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  6. If y=tan^(-1)x , show that (1+x^2)(d^2y)/(dx^2)+2x(dy)/(dx)=0 .

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

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  8. If y=a cos (logx)+b sin (logx), prove that x^(2)y(2)+xy(1)+y=0.

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  9. Find the second derivative of e^(3x)sin4x.

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  10. Find the second derivative of sin 3x cos 5x.

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

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  12. If y=(logx)/x , show that (d^2y)/(dx^2)=(2logx-3)/(x^3) .

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  13. If y=e^(ax)cosb x, Show that (d^2y)/(dx^2)-2a(dy)/(dx)+(a^2+b^2)y=0

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  14. If y=e^acos^((-1)x),-1lt=x<1,s howt h a t (1-x^2)(d^2y)/(dx^2)-x(dy)/...

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  15. If x=a t^2,\ \ y=2\ a t , then (d^2y)/(dx^2)= -1/(t^2) (b) 1/(2\ a t^...

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  16. If x=a (theta-sin theta) and y=a(1-cos theta), find (d^(2)y)/(dx^(2)) ...

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  17. If y=sin(logx) , prove that x^2(d^2y)/(dx^2)+x(dy)/(dx)+y=0 .

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

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  19. If y=e^(x)sinx, prove that (D^(2)y)/(dx^(2))-2(dy)/(dx)+2y=0.

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  20. If x=a(costheta+log(tan(theta/2)) and y=asintheta then find the value ...

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