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Let f(x) be a polynomial.Then, the seco...

Let `f(x)` be a polynomial.Then, the second order derivative of `f(e^x)` is

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RESONANCE DPP-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Statement-1 Let f:[0,oo)vec[0,oo) be a function defined by y=f(x)=x^2,...

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  2. If f(x),g(x),h(x) are polynomials in x of degree 2 and F(x)=|fghf'g' h...

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  3. Let f(x) be a polynomial.Then, the second order derivative of f(e^x) ...

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  4. If f(x)=prod(n=1)^(100)(x-n)^(n(101-n)),w h e r eprod(i=1)^k ai st...

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  5. If the function f(x)=(x^2)/2+lnx+a x is always monotonically increasi...

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  6. fn(x)=e^(f(n-1)(x)) for all n in Na n df0(x)=x ,t h e n d/(dx){fn(x)...

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  7. (d^2x)/(dy^2) equals: (1) ((d^2y)/(dx^2))^(-1) (2) -((d^2y)/(dx^2...

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  8. Find (dy)/(dx) in each of the following cases: y=tan^(-1)(4x)/(1+5x^2...

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  9. If f(x)=lim(n->oo)(3/2+[cosx](sqrt(n^2+1)-sqrt(n^2-3n+1))) whe...

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  10. If g(x)=(2h(x)+|h(x)|)/(2h(x)-|h(x)|) where h(x)=sinx-sin^n x ,n in R...

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  11. If f(x)=|"cos"(x+x^2)"sin"(x+x^2)-"cos"(x+x^2)"sin"(x-x^2)"cos"(x-x^2...

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  12. If y=x/(a+x/(b+x/(a+oo))),t h e nfin d(dy)/(dx)

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  13. Find the sum of the series 1+2x+3x^2+(n-1)x^(n-2) using differentiatio...

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  14. If y=a^x^a^x^...^(((((oo))))) , then prove that (dy)/(dx)=(y^2(log)e ...

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  15. Let f(x)={s in2x ,0<xlt=pi//6a x+b ,pi//6<x<1 . If f(x)a n df^(prime)(...

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  16. If f is twice differentiable such that f^('')(x)=-f(x) and f^(prime)...

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  17. Find (dy)/(dx) if: x=a(cos t+1/2lntan^2t/2) and y=asintdot x=s in tsq...

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  18. If x^m y^n=(x+y)^(m+n), then (dy)/(dx) is (x+y)/(x y) (b) x y (c) x/...

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  19. Let e^(f(x))=lnxdot If g(x) is the inverse function of f(x), then g^(p...

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  20. If y="sec"(tan^(-1)x), then (dy)/(dx) at x=1 is equal to: 1/(sqrt(2)) ...

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