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If y=x^(logx)^(("log"(logdotx))),t h e n...

If `y=x^(logx)^(("log"(logdotx))),t h e n(dy)/(dx)i s` `y/x(1n x^(oox-1))+21 nx1n(1nx))` `y/x(logx)^("log"(logx))(2log(logx)+1)` `y/(x1nx)[(1nx)^2+21 n(1nx)]` `y/x(logy)/(logx)[2log(logx)+1]`

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. Find (dy)/(dx) for y=sin^(-1)(cosx)

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  2. If y=sqrt(x+sqrt(y+sqrt(x+sqrty+...oo))) then (dy)/(dx) equal to

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  3. If y=x^(logx)^(("log"(logdotx))),t h e n(dy)/(dx)i s y/x(1n x^(oox-1)...

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  4. If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+ tooo))) ,prove that (dy)/(dx)=(cos...

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  5. The n t h derivative of x e^x vanishes when (a)x=0 (b) x=-1 (c)...

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  6. If x=a(cost+1/2logtan^2t) and y=asint then find (dy)/(dx) at t=pi/4

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  7. or,find the derivatives of tan^(-1) ((sqrt(1+x^2)-1)/x) with respect t...

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  8. If x^m y^n=(x+y)^(m+n),p rov et h a t(dy)/(dx)=y/xdot

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  9. Let g(x)=f(x)sinx ,w h e r ef(x) is a twice differentiable function on...

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  10. If x=acos^3theta,y=a sin^3theta,then find the value of (d^2y)/(dx^2) a...

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  11. If x = sqrt(a^(sin^(-1)t)) and y= sqrt(a^(cos^(-1)t) show that (dy)/(...

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  12. If x/a+y/b=sqrt2 touches the ellipses x^2/a^2+y^2/b^2=1, then find the...

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  13. If y=f((2x-1)/(x^2+1))andf^'(x)=sinx^2, then find (dy)/(dx)

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  14. Let y=x^(3)-8x+7 and x=f(t)." If "(dy)/(dt)=2 and x=3 at t = 0," then ...

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

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  16. If fr(x),gr(x),hr(x),r=1,2,3 are polynomials such that fr(a)=gr(a)=hr(...

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  17. Find (dy)/(dx)ifx=a(theta-sintheta) and y=a(1-costheta)dot

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  18. If f(x)=(log)x(log x),t h e nf^(prime)(x) at x=e is equal to (a) 1/e ...

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  19. Differentiate tan^(-1)(x/(1+sqrt((1-x^2)))) +{2tan^(-1)sqrt(((1-x)/(1+...

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  20. If x=asec^3theta and y=atan^3theta, find (dy)/(dx) at theta=pi/3dot

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