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(d^(20)y)/(dx^(20))(2cosxcos3x)i se q u ...

`(d^(20)y)/(dx^(20))(2cosxcos3x)i se q u a lto` `2^(20)(cos2x-2^(20)os3x)` `2^(20)(cos2x+2^(20)cos4x)` `2^(20)(sin2x+2^(20)sin4x)` `2^(20)(sin2x-2^(20)sin4x)`

A

`2^(20)( cos 2x -2^(20) cos 3x)`

B

`2^(20)( cos 2x +2^(20) cos 4x)`

C

`2^(20)( sin 2x +2^(20) sin 4x)`

D

`2^(20)( sin 2x - 2^(20) sin 4x)`

Text Solution

Verified by Experts

`y=2cos x cos 3x = cos 4x +cos 2x`
`therefore" "(d^(20)y)/(dx^(20))=4^(20)cos 4x +2^(20) cos 2x`
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CENGAGE-DIFFERENTIATION-Exercise (Single)
  1. If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to n(n-1)y (b...

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  2. Suppose f(x)=e^(a x)+e^(b x) , where a!=b , and that f prime prime(x...

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  3. (d^(20)y)/(dx^(20))(2cosxcos3x)i se q u a lto 2^(20)(cos2x-2^(20)os3x...

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  4. (d^n)/(dx^n)(logx)= ((n-1)!)/(x^n) (b) (n !)/(x^n) ((n-2)!)/(x^n) (d...

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  5. If y=xlog(x/(a+b x)),t h e nx^3(d^2y)/(dx^2)= (a)(x(dy)/(dx)-y)^2 (b)...

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  6. If a x^2+2h x y+b y^2=1,t h e n(d^(2y))/(dx^2) is (h^2-a b)/((h x+b y)...

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  7. If y^(1/m)=(x+sqrt(1+x^2)),t h e n(1+x^2)y2+x y1 is (where yr represen...

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  8. If (sinx)(cosy)=1/2,t h e n(d^2y)/(dx^2)a t(pi/4,pi/4) is -4 (b) -2 (c...

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  9. A function f satisfies the condition f(x)=f^(prime)(x)+f^(x)+f^(x) ,w ...

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  10. Let f(x) be a polynomial of degree 3 such that f(3)=1,f^(prime)(3)=-1,...

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  11. If y^2=a x^2+b x+c ,t h e ny^3(d^(2y))/(dx^2) is a constant a functio...

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  12. If y=sinx+e^x ,t h e n(d^(2x))/(dy^2)= (-sinx+e^x)^(-1) (sinx-e^x)/(...

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  13. If f^(x)=-f(x)a n dg(x)=f^(prime)(x)a n d F(x)=(f(x/2))^2+(g(x/2))^2 ...

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  14. Let y=1n(1+cosx)^2 . Then the value of (d^2y)/(dx^2)+2/(e^(y/2)) equal...

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  15. x=tcost ,y=t+sintdot Then (d^(2x))/(dy^2)at t=pi/2 is (a)(pi+4)/2 (b) ...

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  16. "Let "y=t^(10)+1 and x=t^(8)+1." Then "(d^(2)y)/(dx^(2)) is

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  17. If x = log p and y=(1)/(p), then

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  18. If x=varphi(t), y=psi(t),t h e n(d^(2y))/(dx^2) is (varphi^(prime)psi^...

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  19. If f(x)=x^4tan(x^3)-x1n(1+x^2), then the value of (d^4(f(x)))/(dx^4) ...

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  20. Let g(x) be the inverse of an invertible function f(x), which is diffe...

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