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If `(x-a)^2+(y-b)^2=c^2`, for some `c > 0`, prove that `([1+((dy)/(dx))^2]^(3/2))/((d^2y)/(dx^2))`is a constant independent of a and b.

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-MISCELLANEOUS EXERCISE
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  2. Differentiate w.r.t. x the function (cos^(-1)x/2)/(sqrt(2x+7)),-2<x<2

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

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  4. Differentiate w.r.t. x the function in (logx)^(logx),xgt1.

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  5. Differentiate w.r.t. x the function cos" "(a" "cos" "x" "+" "b" "s in"...

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  6. Differentiate w.r.t. x the function in (sinx-cosx)^((sinx-cosx)),pi/...

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

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

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

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

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

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

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  14. If x=a(cost+tsint) and y=a(sint-tcost), find (d^(2)y)/(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/(dx)(x^n)=n x^(n-1) for all...

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  17. Using the fact that s in (A + B) = s in A cos B + cos A s in Band the ...

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

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

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  20. If y=e^acos^((-1)x),-1lt=x<1,s howt h a t (1-x^2)(d^2y)/(dx^2)-x(dy)/...

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