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If y =e ^(x sin (x ^(3)))+(tan x)^(x) t...

If `y =e ^(x sin (x ^(3)))+(tan x)^(x) ` then `(dy)/(dx)` may be equal to:

A

`e ^(x sin (x^(3)))[3x ^(3) cos (x ^(3))+sin (x ^(3)) ]+ (tan x) ^(x) [ln tan x+ 2x cosec 2x ]`

B

`e ^(x sin (x ^(3)))[x ^(3) cos (x ^(3))+ sin (x ^(3))]+ (tan x )^(x) [ln tan x+ 2x cosec 2x]`

C

`e ^(x sin ( x ^(3)))[x ^(3) sin (x ^(3))+sin (x ^(3))]+(tan x ) ^(x) [ln tan x+2 cosec 2x]`

D

`e ^(xsin (x ^(3)))[3x ^(3) cos (x ^(3))+sin (x ^(3))]+(tan x )^(x) [ln tan x+ (x sec ^(2))/(tan x )]`

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The correct Answer is:
A, D
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VK JAISWAL-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
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  2. Let f(x) =(x^(2)-3x+ 2) (x ^(2) + 3x +2) and alpha, beta, gamma satisf...

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  3. let the function f be defined by f (x)= {{:(p+ qx+ x^(2)"," , x lt 2),...

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  4. If y =e ^(x sin (x ^(3)))+(tan x)^(x) then (dy)/(dx) may be equal to:

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  5. Let f(x)=x+(1-x)x^3+(1-x)(1-x^2)x^3+.........+(1-x)(1-x^2)........(1-x...

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  7. If f (x)= [{:((sin [x^(2)]pi)/(x ^(2)-3x+8)+ax ^(3)+b,,, 0 le x le 1),...

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  8. If f (x)= {{:(1+x, 0 le x le 2),( 3x-2, 2 lt x le 3):}, then f (f(x)) ...

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  9. Let f (x)=(x+1) (x+2) (x+3)…..(x+100) and g (x) =f (x) f''(x) -f ('(x)...

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  10. If f(x)={|x|-3 x < 1|x-2|+a x >= 1 & g(x)={2-|x| x < 2 sgn(x)-b x >= 2...

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  11. Let f (x) be a continous function in [-1,1] such that f (x)= [{:((ln...

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  12. f (x) is differentiable function satisfying the relationship f ^(2) (x...

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  13. The function f (x)=[sqrt(1-sqrt(1-x ^(2)))],(where [.] denotes greates...

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  15. The points of discontinuities of f (x)= [(6x)/(pi)]cos [(3x)/(pi)]"in"...

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  16. If f(x)={{:(,(x^(2))/(2),0 le x lt 1),(,2x^(2)-3x+(3)/(2),1 le x le 2)...

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  17. If x=phi(t),y=Psi(t)," then "(d^(2)y)/(dx^(2)) is equal to

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  18. f (x)=[x] and g (x)= {{:( 0"," , x in I ),( x ^(2)"," , cancel(in)I)...

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  19. Let f : R ^(+) to R defined as f (x)= e ^(x) + ln x and g = f ^(-1) th...

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