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Using mathematical induction prove that ...

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

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PSEB-CONTINUITY AND DIFFERENTIABILITY-Exercise
  1. Differentiate w.r.t. x the function : sin^-1(xsqrtx), 0lexle1

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  2. Differentiate w.r.t. x the function : cos^-1(x/2)/sqrt(2x+7), x lies b...

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  3. Differentiate w.r.t. x the function : cot^-1[(sqrt(1+sinx) + sqrt(1-si...

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  4. Differentiate w.r.t. x the function : (logx)^logx, x>1

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  5. Differentiate w.r.t. x the function : cos(acosx+bsinx), for some const...

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  6. Differentiate w.r.t. x the function : (sinx - cosx)^(sinx-cosx), x lie...

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  7. Differentiate w.r.t. x the function : x^x + x^a + a^x + a^a, for some ...

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

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

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  10. Find dy/dx if y = sin^-1x + sin^-1 sqrt(1-x^2), 0ltxlt1

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  11. If xsqrt(1+y) + ysqrt(1+x) = 0 for x lies between -1 and 1 prove that ...

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

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

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

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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(x^n)/dx = nx^(n-1) for all p...

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  17. Using the fact that sin(A+B) = sinA cosB + cosA sinB and the differen...

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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)],[1,m,n],[a,b,c]|, prove that dy/dx = |[f'(x)...

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  20. If y = e^(acos^-1x), -1lexle1, show that (1-x^2)(d^2y)/dx^2 - x(dy/dx)...

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