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y=logtan(x/2)+sin^(-1)(cosx), then dy/dx...

`y=logtan(x/2)+sin^(-1)(cosx)`, then `dy/dx` is

A

cosec x - 1

B

cosec x

C

cosec x + 1

D

x

Text Solution

Verified by Experts

The correct Answer is:
A
`(dy)/(dx) = (1)/(tan x//2) (sec^(2) (x)/(2))(1)/(2) + (1)/(sqrt(1 - cos^(2) x)) (-sin x)`
` (1)/(2 sin ""(x)/(2) cos "" (x)/(2)) - 1 = " cosec" x - 1 `
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -MHT CET CORER
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  3. y=logtan(x/2)+sin^(-1)(cosx), then dy/dx is

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  4. If x^(2) y^(5) = (x + y)^(7) , " then " (d^(2)y)/(dx^(2)) is equal to

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  5. The equation of tangent to the curve given by x = 3 cos theta , y ...

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  6. Differentiate (logx)^x with respect to logx .

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  7. If x sec theta , y = tan theta , then the value of (d^(2) y)/(dx^(...

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  8. If x=f(t) and y=g(t) , then write the value of (d^2y)/(dx^2) .

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  9. Find (dy)/(dx) , " if x " = 2 cos theta - cos 2 theta and y = 2sin...

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  10. find the derivative of e^(x) + e^(y) = e^(x +y)

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  11. If xy = tan^(-1) (xy) + cot^(-1) (xy), " then" (dy)/(dx) is equal to

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  12. The derivative of cos^(3)x w.r.t. sin^(3)x is

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  13. The derivative of log|x| is

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  14. The function f(x)=e^(-|x|) is

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  15. If f(x)=sin^(-1) ((2x)/(1+x^2)) then f(x) is differentiable on

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  16. If y = log(cos x) sin x " then" (dy)/(dx) is equal to

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  17. If y^(2) = ax^(2) + bx + c , where a,b,c, are constants , then y^...

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  18. If x=phi(t),y=Psi(t)," then "(d^(2)y)/(dx^(2)) is equal to

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  19. If y = 5^(x) x^(5) , " then" (dy)/(dx) is

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  20. If y = tan^(-1) ((a cos x - b sin x)/(b cos x + a sin x)) " then " (dy...

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