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Find derivative of u(x) u( x )= [ ...

Find derivative of u(x) u( x )= [ ln( 1+ sin2x ), if x>0 ` 0,  if x≤0  

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BANSAL-LIMITS AND DERIVATIVES-All Questions
  1. Let f'(x)=3x^2sin1/x-xcos1/x , if x!=0\ ; f(0)=0 and f(1//pi)=0 then: ...

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  2. If f(x)=xdot|x|, then its derivative is : (a)2x (b) -2x (c) 2|x|...

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  3. Find derivative of u(x) u( x )= [ ln( 1+ sin2x ), if x>0 ...

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  4. find v( x )= Lim t→0 2x/ π tan −1 ( 2 /t )

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  5. ("Lim")(n->oo)((1+tanpi/(2n))/(1+sinpi/(3n)))^n equal

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  6. ("Lim")(x->0^+)1/((1+"c o s e c"x)^(1/(ln(sinx)))) equals

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  7. ("Lim")(x->0)(2/picos^(-1)x)^(1//x) equals

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  8. Evaluate: intsqrt((1-sin2x)/(1+sin2x))dx

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  9. Find the differentiation of ((cot^2x-1)/(cot^2x+1)) w.r.t. \ x

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  10. Find the differentiation of sqrt(sec^2x+"c o s e c"^2x) w.r.t. \ x

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  11. Find the differentiation of (1+x^(1/4))(1+x^(1/2))(1-x^(1/4)) w.r.t. \...

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  12. Find the differentiation of (log)(sqrt(x))(1/x) w.r.t. \ x

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  13. Find the differentiation of |x-1|+|x-3| at the point x=2 w.r.t. \ x

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  14. Find the differentiation of cos(1-x^2)^2 w.r.t. \ x

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  15. Find the differentiation of sin^("n")xcosn x w.r.t. \ x

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  16. Find the differentiation of log(sqrt(x-a)+sqrt(x-b)) w.r.t. \ x

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  17. Find the differentiation of (xcot^3x)^(3//2) w.r.t. \ x

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  18. Find the differentiation of sqrt((1+tanx)/(1-tanx)) w.r.t. \ x

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  19. Find the differentiation of (x^2+cosx)^4 w.r.t. \ x

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  20. Find the differentiation of sqrt(xsinx) w.r.t. \ x

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