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The functions u=e^(x).sinx and v=e^(x).c...

The functions `u=e^(x).sinx` and `v=e^(x).cosx` satisfy the equation

A

`v(du)/(dx)-u(dv)/(dx)=u^(2)+v^(2)`

B

`v(d^(2)u)/(dx^(2))=2v`

C

`(d^(2)v)/(dx^(2))=-2u`

D

All of these

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The correct Answer is:
D
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ARIHANT MATHS-DIFFERENTIATION -Exercise (More Than One Correct Option Type Questions)
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  2. If f(x)=sin{(pi)/(3)[x]-x^(2)}" for "2ltxlt3 and [x] denotes the grea...

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  3. The functions u=e^(x).sinx and v=e^(x).cosx satisfy the equation

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  4. If f(x)=log(x^(2))(logx),then f '(x)at x= e is

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  5. Let f be a differentiable function satisfying [f(x)]^(n)=f(nx)" for ...

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  6. If y=f(x) is an odd differentiable function defined on (-oo,oo) such t...

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  7. "If "y=sqrt(x+sqrt(y+sqrt(x+sqrt(y+...oo))))," then prove that "(dy)/(...

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  8. If f(x)=|cosx-sinx| , then f'(pi/4) is equal to

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  9. Let f(x)=x^2+xg'(1)+g''(2) and g(x)=f(1).x^2+xf'(x)+f''(x), then find ...

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  10. if f(x) = x^n then the value of f(1) - (f'(1))/(1!) + (f''(1))/(2!) +...

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  11. If y+log(1+x)=0 which of the following is true?

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  12. If y=2^(3^(x)), then y' equals

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  13. If g is the inverse of fandf(x) = x^(2)+3x-3,(xgt0). then g'(1) equal...

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  14. If x^(3)-2x^(2)y^(2)+5x+y-5=0 and y(1) = 1, then a. y'(1)=(4)/(3) b. y...

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  15. Let y=sqrt(x+sqrt(x+sqrt(x+oo))) , (dy)/(dx) is equal to

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  16. Ify=x^((lnx)^ln(lnx)) , then (dy)/(dx) is equal to

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  17. Which of the following functions are not derivable at x=0?

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  18. If 2^(x)+2^(y)=2^(x+y) then (dy)/(dx)is equal to

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  19. For the function y=f(x)=(x^(2)+bx+c)e^(x), which of the following hold...

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  20. If sqrt(y+x)+sqrt(y-x)=c, where cne0, then (dy)/(dx) has the value equ...

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