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If y = sec^(-1) (frac{sqrt x - 1}{x+sqrt...

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

A

(a) `a`

B

(b) `1/x`

C

(c) `1`

D

(d) `0`

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CHETANA PUBLICATION-Differentiation-Exercise
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  2. If sec(frac{x+y}{x-y}) = a^2, then (d^2 y)/(dx^2) = ............ A) y...

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  3. If y = sec^(-1) (frac{sqrt x - 1}{x+sqrt x}) + sin^(-1) (frac{x + sqr...

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  5. If x^5y = (x+y)^(n-2) and dy/dx = y/x, then n=..........

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  6. If x= e^2log(e)(sin theta), y= e^2log(e)(cos theta), then dy/dx at ...

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  7. If y= sqrt (log x + sqrt (log x + sqrt (log x + .......oo))), then dy/...

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  8. If y= 5^(2log(5)(sin x)) + 7^(2log(7)(cos x)), then dy/dx= A) 1 B) -...

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  9. If y= (sin^(-1) x)^2, then (1-x^2) (d^2 y)/(dx^2) - x (dy/dx) = .........

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  10. If y= sin^(-1) (frac{5x+ 12 sqrt (1-x^2)}{13}), then (dy/dx) = ..........

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  11. If x= a(theta - sin theta), y= a(1- cos theta), then dy/dx=......... A...

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

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

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

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

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

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

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

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  20. 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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