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If y= sin^2 (cot^(-1)sqrt (frac {1+x}{1-...

If y= `sin^2` (`cot^(-1)``sqrt (frac {1+x}{1-x}`)), then `frac{dy}{dx}`=.......

A

(a) `1`

B

(b) `-1`

C

(c) `1/2`

D

(d) `-1/2`

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CHETANA PUBLICATION-Differentiation-Exercise
  1. If x= a cos^3 t, y= a sin^3 t, then dy/dx=..... A) -y/x B) -(y/x)^(1...

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  2. If x^py^q = (x+y)^(p+q), then(d^2y)/(dx^2) =..........

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  3. If y= sin^2 (cot^(-1)sqrt (frac {1+x}{1-x})), then frac{dy}{dx}=.........

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  4. If x = e^theta (sin theta - cos theta), y = e^theta (cos theta + sin t...

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  5. The derivative of cos^(-1)(2x^2 -1) w.r.t. cos^(-1) x is ........... A...

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  6. If x= a(cos t + tsin t), y= a(sin t- t cos t), then dy/dx ...............

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  7. If y= cot^(-1)(frac {1-3x^2}{3x - x^3}), then dy/dx=....... A) frac{3...

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  8. If log (sqrt (x^2 + y^2)) = tan^(-1)(frac{y}{x}), then frac{dy}{dx} is...

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  9. If x= a(t-1/t), y=a(t+1/t), then dy/dx =........ A) x/y B) y/x C) ...

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  10. If x^2 + 6xy + y^2 = 10, then frac{d^2y}{dx^2} =..........

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  11. If e^y = (x+1) then (d^2y)/(dx^2) =.......... A) (dy/dx)^2 B) -(dy/dx)...

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  12. If x= a(cos theta + sin theta), y= a(sin theta + cos theta), then [(d^...

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  13. If x^y = e^(x-y), then dy/dx = ............ A) frac {log x}{(1+logx)...

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  14. If y is a function of x and log(x+y) = 2xy, then the value of y'(0) = ...

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  15. If y= cos(x^2 + a^2) find dy/dx

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  16. Differentiate tan^(-1) (sqrt x) w.r.t. x

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  17. Find dy/dx, if x= cosec^2theta, y= cot^3theta, at theta = (pi)/6

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  18. Differentiate x^x w. r. t. x

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  19. Find dy/dx if y= sin^(-1)(3x-4x^3)

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  20. Find (d^2y)/(dx^2) if y= log(log x)

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