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If f(xy)=(f(x))/y+(f(y))/x holds for all...

If `f(xy)=(f(x))/y+(f(y))/x` holds for all real `x` and `y` greater than `0` and `f(x)` is a differentiable function for all `x >0` such that `f(e)=1/e` , then find `f(x)`

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. If y^x=x^y ,"then find"(dy)/(dx)dot

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  2. Differentiate (xcosx)^x with respect to xdot

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  3. If f(xy)=(f(x))/y+(f(y))/x holds for all real x and y greater than 0 a...

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  4. Find (dy)/(dx) for y=x^xdot

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  5. If Pn is the sum of a GdotPdot upto n terms (ngeq3), then prove that (...

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  6. If y=f(a^x)a n df^(prime)(sinx)=(log)e x ,then f i n d ((dy)/(dx)), if...

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  7. if x<1 then 1/(1+x)+(2x)/(1+x^2)+(4x^3)/(1+x^4)+..............oo

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  8. Find the derivative of (sqrt(x)(x+4)^(3/2))/((4x-3)^(4/3))

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  9. If ("lim")(tvecx)(e^tf(x)-e^xf(t))/((t-x)(f(x))^2)=2a n df(0)=1/2, the...

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  10. If y=x^(x^(x^x...oo) , find (dy)/(dx)

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  11. If y=e^(sqrt(x))+e^(-sqrt(x)) , then (dy)/(dx) is equal to (a)(e^(sqr...

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  12. Differentiate sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5))) with respect to x

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  13. If f(x)=|sinx-|cosx||, then the value of f^'(x) at x=(7pi)/6 is (a) ...

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  14. If y=(tanx)^((tanx)^((tanx).... ∞) ,then find (dy)/(dx) at x=pi/4

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  15. If graph of y=f(x) is symmetrical about the y-axis and that of y=g(x)...

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  16. Differentiate the function with respect to x using the first principle...

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  17. If x=t^2,y=t^3,t h e n(d^2y)/(dx^2)= (a)3/2 (b) 3/((4t)) (c) 3/(2...

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  18. Using the first principle, prove that: d/(dx)(f(x)g(x))=f(x)d/(dx)(g(x...

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  19. If y=x+e^x, then (d^2x)/(dy^2) is (a) e^x (b) - e^x/((1+e^x)^3) (c) -e...

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  20. If y=(1+x^(1/4))(1+x^(1/2))(1-x^(1/4)) , then find (dy)/(dx)dot

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