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

Let `f(x)` be a polynomial.Then, the second order derivative of `f(e^x)` is `f^(e^x)e^(2x)+f^(prime)(e^x)e^x` `f^(e^x)e^x+f^(prime)(e^x)` `f^(e^x)e^(2x)+f^(e^x)e^x` (d) `f^(e^x)`

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RESONANCE DPP ENGLISH-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)a n dh(x) are three polynomial of degree 2, then prove t...

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

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  4. about to only mathematics

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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: ((d^2y)/(dx^2))^(-1) (b) -((d^2y)/(dx^2))^(-1)(...

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  8. y=tan^(-1)""(4x)/(1+5x^(2))+tan^(-1)""(2+3x)/(3-2x)

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  9. If f (x) =lim (x to oo) x ((3)/(2) + [cos x)(sqrt(n^(2) +1)-sqrt(n ^(2...

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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 If {:(" ""x"),(y=""),(" ""x"),(" ""a+")...

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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), f'(x)=g(x), h'(x...

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  17. Find (dy)/(dx) : x=a{cost+1/2logt a n^2t/2} and y=asint .

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  18. If x^m y^n=(x+y)^(m+n), prove that (dy)/(dx)=y/x .

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  19. If e^f(x)= log x and g(x) is the inverse function of f(x), then g'(x)...

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

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