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If x = sec theta - cos theta = y = sec '...

If `x = sec theta - cos theta = y = sec ''theta - cos ^(n) theta ` then show that ` ((dy)/(dx)) ^(2) = (n ^(2) ( y ^(2) + 4))/(x ^(2) + 4)`

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AAKASH SERIES-DIFFERENTIATION -EXERCISE -4.7
  1. If x =a ( t - sint ) , y =a ( 1 + cos t ) find (d ^(2) y )/(dx ^(2))...

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  2. (d)/(dx) {Tan ^(-1) ((1+x)/(1- x))}=

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  3. (d)/(dx) {Tan ^(-1) ""(2x)/(1- x ^(2))}=

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  4. Tan^(-1)((3x-x^(3))/(1-3x^(2)))=

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  5. If y=e ^(-2x) sin ^(3) x, then (d^(2)y)/dx^(2)=

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  6. Find the second derivative of e ^(x) sin x cos 2x .

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  7. If y=128 sin ^(3) x cos ^(4) x ,then find (d^(2)y)/dx^(2)

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  8. sin 2x.sin 3x.sin 4x

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  9. Show that y=x+tanx satisfies the equation cos^(2)x(dy^(2))/(dx^(2))+2x...

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  10. If y=sin(sinx) then show that y''+(tanx)y'+ycos^(2)x=0.

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  11. If y =a cos x + (b + 2x) sin x then show that y" + y=4 cos x.

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  12. If y=sin(sinx) then show that y''+(tanx)y'+ycos^(2)x=0.

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  13. If y = e ^(-kx //2) (a cos nx + b sin nx) then y (2)+ky(1)+ (n^(2) + k...

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  14. If y=ax^(n+1)+bx^(-n) then show that x^(2)y''=n(n+1)y.

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  15. If y =6 (x +1) + (a+ b x) e ^(3x) then show that y" v + y = 4x + 8

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  16. If x = sec theta - cos theta = y = sec ''theta - cos ^(n) theta then ...

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  17. If y = Tan ^(-)x then show that (1 + x ^(2)) y (2) + 2xy (1) = 0

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  18. If y = (sin ^(-1) x ) ^(2) then show that (1- x ^(2)) y (2) - xy(1) = ...

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  19. If y = (x+ sqrt(x ^(2) -1))^(m) then (x ^(2) -1) y(2) + xy (1)=

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  20. If y =e ^( m Cos ^(-1)x) then show that (1- x^(2)) y (2) - xy(1) -m^(2...

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