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If `y=f(x)` satisfies `f(x+y)=2f(x)+xf(y)+y(f(x))^(1//3` for all `x, y in R,f'(0)=0` then `(f(2))^(2)` is equal to

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MCGROW HILL PUBLICATION-DIFFERENTIABILITY AND DIFFERENTIATION -EXERCISE (LEVEL 1) Single Correct Answer Type Questions
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  2. The derivative of sin^(-1)((1-x^(2n))/(1+x^(2n))) with respect to x^(2...

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  3. If sqrt(1-x^(6))+sqrt(1-y^(6))=a(x^(3)-y^(3)) and (dy)/(dx)=f(x,y)sqrt...

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  4. If f(x)=x^(2)+tan x and f is inverse of g, then g'(x) is equal to

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  5. Number of points of non-differentiability of f(x)=sin pi(x-[x]) in (-p...

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  6. Suppose that f is differentiable function with the property f(x+y)=f(x...

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  7. If y=f(x) satisfies f(x+y)=2f(x)+xf(y)+y(f(x))^(1//3 for all x, y in R...

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  8. If f(0)=0,f'(0)=4 and g(x)=f(-x+fof(x)) then g'(0) is equal to

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  9. If f(x)=x^(6)+e^(x//7) and fog(x)=x^(3), then g'(1) is equal to

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  10. Let (a-b cos y)(a+b cos x)=a^(2)-b^(2) and (dy)/(dx)=((sinx)f(y))/((a+...

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  11. If y=(x^(2)+1)sinx then [y(18)"("pi//2+((pi^(2))/(4)+1)] is equal to

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  12. If f(x)=cos^(2)x+cos^(2)((pi)/(3)+x)-cosx cos((pi)/(3)+x) then f(pi//8...

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  13. If y=3t-t^(3),x=3t^(2) satisfies Ay(2)(y-sqrt(3x))=x+3 then A is equal...

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  14. If f and g are two functions having derivative of order three for all ...

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  15. If y=sin^(-1)sqrt((1-x)/(1+x)) then "|"(dy)/(dx)|(x=1//2)| is equal to...

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  16. Suppose that f is differentiable function with the property f(x+y)=f(x...

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  17. If y=rx and x=tx, all variables being functions of x. If suffixes deno...

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  18. Let (a-b cos y)(a+b cos x)=a^(2)-b^(2) and (dy)/(dx)=(sin x f(y))/((a+...

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  19. Let f be a differentiable function whose range is contained in [0,oo) ...

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  20. Let f be a differentiable function satisfying f(-x)f'(x)=f(x)f'(-x) fo...

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