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Differentiate tan^(-1)((2^(x+1))/(1-4^(x...

Differentiate `tan^(-1)((2^(x+1))/(1-4^(x)))` with respect to x.

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The correct Answer is:
`(2^(x+1)log2)/(1+4^(x))`
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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(f) (LONG ANSWER TYPE QUESTIONS (I))
  1. Differentiate the following w.r.t. x : e^(sec^(2)x)+3cos^(-1)x.

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  2. Differentiate the following w.r.t. x : log(sinsqrt(1+x^(2)))

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  3. Differentiate the following w.r.t. x : sin(logx),xgt0

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  4. Differentiate the following w.r.t. x : log(cos5x)

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  5. Differentiate the following w.r.t. x : cot(logx+e^(sqrtx))

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  6. Differentiate the following w.r.t. x : 2l(n)((x-1)/(x+1))

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  7. Differentiate the following w.r.t. x : x^(2)l(n)(sqrt((x^(2)+9)/(x^(...

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  8. Differentiate the following w.r.t. x : ln(secx+tanx)

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  9. Differentiate the following w.r.t. x : l(n)(sqrt((1-cosx)/(1+cosx)))

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  10. Differentiate the following w.r.t. x : log((1+x)/(1-x))

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  11. Differentiate the following w.r.t. x : logtan(pi/4+x/2)

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  12. Differentiate the following w.r.t. x : log((x+sqrt(x^(2)-a^(2)))/(x-...

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  13. Differentiate the following w.r.t. x : logsin^(-1)(2xsqrt(1-x^(2)))

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  14. Differentiate the following w.r.t. x : sqrt(log(sin(x^(2)/3-1)))

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  15. Find dy/dx when : siny+logy=x^(2)+18x+3

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  16. Find dy/dx when : xy+xe^(-y)+ye^(x)=x^(2).

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  17. if e^(x+y)=x y , show that (dy)/(dx)=(y(1-x))/(x(y-1))

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  18. if y=(sin^(- 1)x)/(sqrt(1-x^2)), prove that (1-x^2)(dy)/(dx)=x y+1

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  19. If x=tan(1/alogy), show that (1+x^(2))dy/dx=ay.

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  20. Differentiate tan^(-1)((2^(x+1))/(1-4^(x))) with respect to x.

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