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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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(d^(20))/(dx^(20))(2cos x cos3x) is equal to (a) 2^(20)(cos2x-2^(20)cos3x)(b)2^(20)(cos2x+2^(20)cos4x)(c)2^(20)(cos2x+2^(20)sin4x)(d)2^(20)(sin2x-2^(20)sin4x)

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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^(ax) + e^(bx), where a!=b, and that fprimeprime(x)-2fpr...

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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. The n t h derivative of the function f(x)=1/(1-x^2)[w h e r ex in (-1,...

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  6. If y=xlog"{"x/((a+b x))"]" , then show that x^3(d^2y)/(dx^2)=(x(dy)/(d...

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  7. 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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  8. "If "y^(1//m)=(x+sqrt(1+x^(2)))," then "(1+x^(2))y(2)+xy(1) is (where ...

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

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

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  12. If y^2=a x^2+b x+c , then y^3(d^2y)/(dx^2) is (a) a constant (b) a fun...

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

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  14. If y= sin px and y(n) is the n^(th) derivative of y, then |{:(y,y(1)...

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

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  17. x=tcost ,y=t+sintdot Then (d^(2x))/(dy^2)a tt=pi/2 is (pi+4)/2 (b) -(p...

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  18. "If "f(x)=(x-1)^(4)(x-2)^(3)(x-3)^(2)(x-4), then the value of f'''(1)+...

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  19. let y=t^(10)+1, and x=t^8+1, then (d^2y)/(dx^2) is

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

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