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Prove that , if y=logtan((pi)/(4)+(x)/(2...

Prove that , if `y=logtan((pi)/(4)+(x)/(2))` , then `(dy)/(dx)=secx`

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ARIHANT PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-Topic 2 (practice question (4 mark question)
  1. Find (dy)/(dt), when y=sin^(-1)(2sqrt(t^(2)-1)/(t^(2)))

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  2. Find dy/dx if x^m y^n = (x/y)^(m+n)

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  3. Find (dy)/(dx), when y^(x)=x^(siny)

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  4. Find the dy/dx when cos x = sqrt ((1)/(1+t^2)), sin y = (2t)/(1+t^2)

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  5. If y=cosec^(-1)x, then find (dy)/(dx) and determine its value at x=-2.

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  6. Examine the differentiability to log|x| for all real values of x.

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  7. Find the derivative of x^(sinx) w.r.t.x.

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  8. Differentiate. sin^(-1)((2x)/(1+x^2))w.r.t.cos^(-1)((1-x^2)/(1+x^2))

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  9. If cos y = x cos(a+y) then prove that dy/dx = (cos^2(a+y))/sin a

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  10. Prove that , if y=logtan((pi)/(4)+(x)/(2)) , then (dy)/(dx)=secx

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  11. Differentiate y=2^(x^(2))+tan^(-1)((cosx-sinx)/(cos x+sinx)) w.r.t. x.

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  12. Write, why the function sin^(-1)((1)/(sqrt(1-x^(2)))) cannot be differ...

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  13. Prove that y=tan(x+y), then (dy)/(dx)=(1+y^(2))/(-y^(2))

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  14. Find the derivative of tan^(-1)(1+x^(2)) with respect to log(x^(2)+1)

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  15. If y=sin^(-1)((2sqrt(x^(2)-1))/(x^(2))) , then find (dy)/(dx).

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  16. Find dy/dx, sinx=(2t)/(1+t^2),tany=(2t)/(1-t^2)

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  17. If y=(x)/(x+2) then prove that x(dy)/(dx)=(1-y)y.

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  18. Find the derivative of (sinx)^(cosx) w.r.t.x.

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  19. If f(x)=xcosx+e^(x) , then find f.(0).

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  20. Differentiate (x)/(sinx) with respect to sinx.

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