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Using mathematical induction prove that `(d)/(dx)(x^n)= nx^(n-1)` for all positive integers n.

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NCERT BANGLISH-CONTINUITY AND DIFFERENTIABILITY-MISCELLANEOUS EXERCISE ON CHAPTER 5
  1. Differentiate w.r.t.x the function in Exercises 1 to 11. sin^(-1)(x ...

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  2. Differentiate w.r.t.x the function in Exercises 1 to 11. (cos^(-1)""...

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  3. Differentiate w.r.t.x the function in Exercises 1 to 11. cot^(-1)[(s...

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  4. Differentiate w.r.t.x the function in Exercises 1 to 11. (x)^(log x)...

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  5. Differentiate w.r.t.x the function in Exercises 1 to 11. cos( a cos ...

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  6. Differentiate w.r.t.x the function in Exercises 1 to 11. (sin x- cos...

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  7. Differentiate w.r.t.x the function in Exercises 1 to 11. x^(x)+x^(a)...

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  8. x^(x^(2)-3)+(x-3)^(x^2)," for "x gt 3.

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  9. Find (dy)/(dx), " if "y=12 (1-cos t), x= 10(t-sin t), -(pi)/(2) lt t l...

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  10. Find (dy)/(dx)," if "y= sin^(-1)x +sin^(-1)sqrt(1-x^(2)), 0 lt x lt 1.

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  11. If xsqrt(1+y)+ysqrt(1+x)=0," for ", -1 lt x lt 1, prove that (dy)/(d...

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  12. If (x-a)^(2)+(y-b)^(2)=c^(2), for some c gt 0, prove that ([1+((dy)/...

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  13. If cos y= x cos (a+y), with cos a ne pm 1, prove that (dy)/(dx)=(cos^(...

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

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  15. If f(x)= |x|^(3), show that f''(x) exists for all real x and find it.

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  16. Using mathematical induction prove that (d)/(dx)(x^n)= nx^(n-1) for al...

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  17. Using the fact the that sin (A+B)= sin A cos B+ cos A sin B and the di...

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  18. Does there exist a function which is continuous everywhere but not dif...

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  19. If y=|{:(f(x),g(x),h(x)),(l,m,n),(a,b,c):}|, prove that (dy)/(dx)=|{:(...

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  20. If y= e^(a cos^(-1)x), -1 le x le 1, show that (1-x^(2))(d^(2)y)/(dx^(...

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