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For a positive constant a find (dy)/(dx)...

For a positive constant a find `(dy)/(dx)` , where `y=a^(t+1/t)` and `x=(t+1/t)^a` .

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BANSAL-LIMITS AND DERIVATIVES-All Questions
  1. If e^y(x+1)=1 . Show that (d^2y)/(dx^2)=((dy)/(dx))^2

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  2. If y=(tan^(-1)x)^2 , show that (x^2+1)^2y2+2x(x^2+1)y1=2 .

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  3. For a positive constant a find (dy)/(dx) , where y=a^(t+1/t) and x=(t+...

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  4. Differentiate sin^2x w.r.t. e^(cosx) .

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  5. Find (dy)/(dx) , if y=12(1-cost) , x=10(t-sint)

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  6. Find (dy)/(dx) , if y=sin^(-1)x+sin^(-1)sqrt(1-x^2) , -1lt=xlt=1

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  7. If xsqrt(1+y)+ysqrt(1+x)=0, prove that (dy)/(dx)=-1/((x+1)^2)

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  8. If cosy=xcos(a+y) , with cosa!=+-1 , prove that (dy)/(dx)=(cos^2(a+...

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  9. If x=a(cost+tsint) and y=a(sint- tcost) , find (d^2y)/(dx^2) .

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  10. If y=e^acos^((-1)x) , -1lt=xlt=1 , show that (1-x^2) (d^2y)/(dx^2)-x(d...

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  11. If y=|sinxcosxsinxcosx-sinxcosxx1 1| , find (dy)/(dx) .

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  12. if =|{:(x^(n),,n!,,2),(cos x,,cos.(npi)/(2),,4),(sin x,,sin .(npi)/(2)...

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  13. If (1+x)^n=C0+C1+C2\ x^2+\ dot+Cn\ x^n , using derivatives prove th...

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  14. If f,g,a n dh are differentiable functions of xa n d(x)=|fgh(xf)'(x...

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  15. If f(x)=|"cos"(x+x^2)"sin"(x+x^2)-"cos"(x+x^2)"sin"(x-x^2)"cos"(x-x^2...

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  16. Let alpha be a repeated root of a quadratic equation f(x)=0a n dA(x...

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  17. Evaluate ("Lim")(x->0)(xcosx-"ln"(1+x))/(x^2)

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  18. Evaluate find a and b if \ ("Lim")(x->0)(x(1+acosx)-bsinx)/(x^3)=1

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  19. ("Lim")(x->0)(e^xsinx-x-x^2)/(x^2+x-"ln"(1-x))

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  20. Evaluate: ("Lim")(x->0)(1+sinx-cosx+"ln"(1-x))/(xtan^2x) -1/2 (b)...

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