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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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V PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Differentiate the following w.r.t. x (i) cos ^(-1)(sin x) (if) tan ^...

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  2. Find f'(x) if f(x)=(sin x)^(sin x) for all 0ltxltpi

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

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

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  5. Differentiate w.r.t x the function (3 x^2-9 x+5)^9

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  6. Differentiate w.r.t x the function sin ^3 x+cos ^6 x

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  7. Differentiate w.r.t x the function (5 x)^(3 cos 2 x)

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  8. Differentiate w.r.t x the function sin ^(-1)(x sqrt(x)), 0 le x le 1

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  9. Differentiate w.r.t x the function cos ^(-1)(x/2)/(sqrt(2 x+7))

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  10. Differentiate w.r.t x the functions cot ^(-1)[(sqrt(1+sin x)+sqrt(1-si...

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  11. Differentiate w.r.t x the function (log x)^(log x), x>1

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  12. Differentiate w.r.t x the function cos (a cos x+b sin x), for some co...

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  13. Differentiate w.r.t x the function (sin x-cos x)^((sin x-cos x))

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  14. Differentiate the following w.r.t.x x^x+x^a+a^x+a^a for some fixed agt...

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  15. Differentiate w.r.t x the function x^(x^2-3)+(x-3)^(x^2), for x>3

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  16. Find dy/dx,if y=12(1-cost),x=10(t-sint).pi/2lttltpi/2

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  17. Find (dy/dx), if y=sin ^(-1) x+sin ^(-1) sqrt(1-x^2),-1 le x le 1

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  18. if x sqrt(1+y)+ysqrt(1+x)=0 prove that (dy/dx)=-1/(1+x)^2

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  19. if (x-a)^2+(y-b)^2=c^2, for some c>0 prove that [1+(dy/dx)^2]^(3/2) /(...

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  20. If cos y=x cos (a+y) prove that (dy/dx)=(cos ^2(a+y))/sina

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