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Let f be a function such that f(x+y)=f(x...

Let `f` be a function such that `f(x+y)=f(x)+f(y)` for all ` x and y and f(x)=(2x^2+3x)g(x)` for all`x ,` where `g(x)` is continuous and `g(0)=3.` Then find `f^(prime)(x)dot`

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. Let g: RvecR be a differentiable function satisfying g(x)=g(y)g(x-y)AA...

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  2. If f,g,a n d \ h are differentiable functions of x and d(x)=|[f,g,h]...

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  3. Let f be a function such that f(x+y)=f(x)+f(y) for all x and y and f(...

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  4. If f((x+y)/3)=(2+f(x)+f(y))/3 for all x,y f'(2)=2 then find f(x)

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  5. Prove that lim(x->0) (f(x+h)+f(x-h)-2f(x))/h^2 = f''(x)

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  6. Let f(x+y)=f(x)+f(y)+2x y-1 for all real x and y and f(x) be a differe...

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  7. If x=e^(y+e^(y+e^y....oo) , where x &gt0,then find(dy)/(dx)

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  8. Let f: RvecR be a function satisfying condition f(x+y^3)=f(x)+[f(y)]^3...

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  9. If x y=e^((x-y)), then find (dy)/(dx)

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  10. (dy)/(dx) for y=tan^(-1){sqrt((1+cosx)/(1-cosx))} ,where 0 lt x lt pi,...

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  11. If y^x=x^y ,"then find"(dy)/(dx)dot

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

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

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

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

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

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

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  19. Find ("lim")(xto2)(xf(2)-2f(x))/(x-2) if f(2)=4 and f′(2)=1

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

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