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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 PUBLICATION-DIFFERENTIATION-Execrises
  1. If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to (a) n(n-1)...

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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)=? (a)((n-1)!)/(x^n) (b) (n !)/(x^n) (c)((n-2)!)/(...

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  5. "If "y= xlog ((x)/(a+bx))," then "x^(3)(d^(2)y)/(dx^(2))=

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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)))," then "(1+x^(2))y(2)+xy(1) is (where ...

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  8. If ( sin x) (cos y) = 1//2, then d^(2)y//dx^(2) at (pi//4, pi//4) is

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

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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)=ax^(2)+bx+c," then "y^(3)(d^(2)y)/(dx^(2)) is

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  12. "If "y= cos x +e^(4x)," then "(d^(2)y)/(dx^(2))=

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  13. If '' (x)=-f(x) and g(x)=-f'(x) and F(x)=(f(x/2))^2 + (g(x/2))^2 and ...

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

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

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  16. "Let "y=t^(12)+1 and x=t^(6)+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^2 y)/(dx^2) is (a)(varphi^(prime)ps...

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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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