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A function f:R rarr R" satisfies the equ...

A function `f:R rarr R"` satisfies the equation `f(x+y)=f(x)f(y)` for all values of `x" and "y` and for any `x in R,f(x)!=0`. Suppose the function is differentiable at `x=0" and "f'(0)=2`, then for all `x in R,f(x)=`

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A DAS GUPTA-Differentiation-Exercise
  1. A function f:R rarr R" satisfies the equation f(x+y)=f(x)f(y) for all ...

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  2. Differentiate the function w.r.t x : x^2cos x

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  3. Differentiate the function w.r.t x :cos^-1 (x^(x^2))

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  4. Differentiate the function w.r.t x :cos^-1 (e^sqrt(tanx))

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  5. Differentiate the function w.r.t x :root(3)(sinx)

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  6. Differentiate the function w.r.t x :e^(x^2)

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  7. Differentiate the function w.r.t x :logx/x

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  8. Find the derivatives w.r.t x at the indicated points : xtan^-1x at x=...

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  9. Find the derivatives w.r.t x at the indicated points : log |x | at x=...

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  10. Find the derivatives w.r.t x at the indicated points : |x-1| + |x-3| ...

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  11. Find the derivatives w.r.t x at the indicated points : |cos x| at x=(...

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  12. Find the derivatives w.r.t x at the indicated points : sin(log x) at ...

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  13. If f(x)=x+log|x|, x!=0 find f'(x).

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  14. If y=2/(sqrt (a^2-b^2)) tan ^-1 [(sqrt( a-b)/(a+b)) tan x/2], show tha...

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  15. Show that y= Asin x + Bcos x + xsin x is a solution of differential eq...

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  16. Show that, v = A/r + B satisfies the differential equation (d^2v)/(dr...

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  17. If y=(ax^2)/((x-a)(x-b)(x-c))+(bx)/((x-b)(x-c))+c/(x-c)+1 then (y prim...

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  18. If y=sqrt (a^2-x^2)+a/2 log ((a-sqrt(a^2-x^2))/(a+sqrt(a^2-x^2))), the...

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  19. Find (dy)/(dx), if y=sin^(-1)[xsqrt(\ 1-x)-\ sqrt(x)\ sqrt(1-x^2)\ ]\

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  20. "if y"="cos"^(-1)((5"cos" x-12 "sin"x)/(13)), where x in (0,(pi)/(2)...

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  21. Find dy/dx if y is equal to : (xlogx)^loglog x

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