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If y=cos^-1[(1-x^2)/(1+x^2)] Put x=tanth...

If `y=cos^-1[(1-x^2)/(1+x^2)]` Put `x=tantheta` and prove that `y=2tan^-1x`.

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BODY BOOKS PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Consider the function f(x)={(1+x,xle2),(5-x,x>2):} Check the different...

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  2. Consider the function f(x)={(1+x,xle2),(5-x,x>2):} Check the different...

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  3. If y=cos^-1[(1-x^2)/(1+x^2)] Put x=tantheta and prove that y=2tan^-1x.

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  4. If y=cos^-1[(1-x^2)/(1+x^2)] Find dy/dx.

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  5. Let siny=xsin(a+y) Express x as a function of y.

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  6. If siny=xsin(a+y), prove that (dy)/(dx)=(sin^2(a+y))/(sina)

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  7. Consider f:[3,infty)to[1,infty) given by f(x)=x^2-6x+10. Find f^-1

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  8. Find dy/dx if x^(2//3)+y^(2//3)=a^(2//3), where a is a constant.

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  9. Find the derivative of log(tan e^x) w.r.t.x.

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  10. Find (dy)/(dx) if 2x+3y=sinx

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  11. Consider the parametric functions x=acos^3theta and y=bsin^3theta. Fin...

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  12. Consider the parametric functions x=acos^3theta and y=bsin^3theta. Sho...

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  13. Differentiate the following. e^(ax).cos(bx+c).

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  14. Differentiate the following. sin[sqrt(sinsqrtx)].

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  15. If y=x^(x^x). Prove that logy=x^x(logx)

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  16. If y=x^(x^x) Find dy/dx.

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  17. Consider y=tan^-1sqrt((1+sinx)/(1-sinx)) . Hence prove that y=pi/4+x/2...

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  18. Consider y=tan^-1sqrt((1+sinx)/(1-sinx)) Find dy/dx.

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  19. sin(xy)+x/y=x^2-y. Evaluate dy/dx

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  20. Given x^y=y^x. Take logarithm of both sides.

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