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`d/(dx)[cos^(-1)(xsqrt(x)-sqrt((1-x)(1-x^2)))]=` `1/(sqrt(1-x^2))-1/(2sqrt(x-x^2))` `(-1)/(sqrt(1-x^2))-1/(2sqrt(x-x^2))` `1/(sqrt(1-x^2))+1/(2sqrt(x-x^2))` `1/(sqrt(1-x^2))` `0` b. `1//4` c. `-1//4` d. none of these

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Simplify : (a) sqrt(y+sqrt(2xy-x^(2))) + sqrt(y-sqrt(2xy-x^(2))) (b) (x+sqrt(x^2-1))/(x-sqrt(x^(2)-1)) -(x-sqrt(x^(2)-1))/(x+sqrt(x^(2)-1))

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CENGAGE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-All Questions
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  2. If y=x^((log x)^(log(log,x)))," then "(dy)/(dx) is

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  3. d/(dx)[cos^(-1)(xsqrt(x)-sqrt((1-x)(1-x^2)))]= 1/(sqrt(1-x^2))-1/(2s...

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  4. Let g(x)=e^(f(x)) and f(x+1)=x+f(x) AA x in R. If n in I^(+)", then"(g...

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  5. Let g(x) be the inverse of f(x) and f'(x)=1/(1+x^3). Then find g'(x) i...

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  9. f is a strictly monotonic differentiable function with f^(prime)(x)=1/...

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  14. If 'f' is an increasing function from RtoR such that f^(prime)prime(x)...

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  15. If x=(1+t)/(t^(3)),y=(3)/(2t^(2))+(2)/(t) then x((dy)/(dx))^(3)-(dy)/(...

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  16. Let f(x)={2/(1+x^2),xi sr a t ion a l b ,xi sr a t ion a l has exactly...

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