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Differential coefficient of sqrt(secsqr...

Differential coefficient of ` sqrt(secsqrt (x))` is

A

`(1)/(4 sqrt(x)) sec sqrt(x) sin sqrt(x)`

B

`(1)/(4 sqrt(x)) (sec sqrt(x))^(3//2). sin sqrt(x)`

C

`(1)/(2) sqrt(x)sqrt(x) sin sqrt(x)`

D

`(1)/(2) sqrt(x)(sec sqrt(x))^(3//2). sin sqrt(x)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let ` y = sqrt( sec sqrt(x)`
` rArr (dy)/(dx) = (1)/(2sqrt(sec sqrt(x)) )(d)/(dx) (sec sqrt(x))`
`rArr (dy)/(dx) = (1)/(2sqrt(sec sqrt(x))). sec sqrt(x). tan sqrt(x) . (1)/(2sqrt(x))`
` (1)/(4sqrt(x)) (sec sqrt(x))^(3//2) . sin sqrt(x)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -EXERCISE 1 DERIVATIVE OF COMPOSITE FUNCTION (BY CHAIN RULE )
  1. Derivative of 2sqrt(cot(x^(2))) with respect to x is

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  2. Derivative of sqrt( tan sqrt(x)) with respect to x is

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  3. If f(x)=sqrt(1+cos^2(x^2)),t h e nf^(prime)((sqrt(pi))/2) is

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  4. If y = sqrt(sin + y ) "then" (dy)/(dx) is equal to

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  5. The differential coefficient of sin (cos (x^(2))) with respect to s i...

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  6. If y=sqrt(x(log)e x) , then find (dy)/(dx) at x=e .

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  7. If y= ( cos x ^(2))^(2) , "then" (dy)/(dx) is equal to

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  8. If y=cos(sinx^2) then at x=sqrt(pi/2), (dy)/(dx)=

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  9. Derivative of log[log(log x^(5))] with respect to x is

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  10. If f(x) = log(x^(2)) (log(e) x) "then f' (x) at x= e" is

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  11. If y = log(2) log(2) (x) , " then " (dy)/(dx) is equal to

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  12. If x=(1-sqrt(y))/(1+sqrt(y)) then (dy)/(dx) is equal to

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  13. If y = log (sin (x^(2))), 0 lt x lt (pi)/(2), "then " (dy)/(dx) "at ...

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  14. (d)/(dx)[log(e)e^(sin(x^(2)))] is equal to

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

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  16. Differential coefficient of sqrt(secsqrt (x)) is

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  17. (d)/(dx) [ log{e^(x) ((x-2)/(x +2))^(3//4)}] is equal to

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  18. Derivative of sqrte^(sqrt(x)) with respect to x is

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  19. The derivative of y = sec^(-1) ((1)/(8x)) is

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  20. If y = sin^(-1) (cos x) , then derivative of y is

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