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Differentiate w.r.t x the function x^(x^...

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

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

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

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

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

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

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

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

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  9. If x=a(cos t+t sin t) and y=a(sin t-t cos t), find (d^2y)/(dx^2)

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  10. Using mathematical induction prove that d/(d x)(x^n)=n x^(n-1) for all...

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  11. Using the fact that sin (A+B)=sin A cos B+cos A sin B and the techniqu...

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  12. "All continuous function are not differentiable." Justify your answe...

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  13. If y=|[f(x), g(x), h(x)],[ l, m , n],[ a , b , c]| prove that (dy/...

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  14. If y=e^(acos^-1x) , then show that (1-x^2)y2-xy1-a^2y=0

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  15. Let y=(x+sqrt(1+x^2))^m i) Find (dy/dx) ii) Show that (1+x^2) (d^2 y...

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  16. Let y=tan ^(-1)((1-cos x)/(sin x)) i) Express 1-cos x and sinx in ter...

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  17. If x y=a x^2+b/x, prove that x^2 y2+2(x (dy/dx)-y)=0

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  18. Establish that g(x)=1-x+absx is continious at origin.

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  19. a) Find (dy/dx) if i) y=sin (x^3+7) ii) x=a(t-sin t), y=a(1-cos t) ...

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  20. Discuss the continuity of the function f(x)={(sin x/x , if , x<0),( ...

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