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

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

A

-2

B

2

C

` - 2 sqrt((pi)/(2))`

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
` because y = cos (sin x^(2))`
` therefore (dy)/(dx) = - sin (sin x^(2)) cos x^(2) . 2x `
` At x = sqrt((pi)/(2)),(dy)/(dx) = - sin (sin"" (pi)/(2)) cos"" (pi)/(2) . 2. sqrt((pi)/(2)) = 0 `
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -EXERCISE 1 DERIVATIVE OF COMPOSITE FUNCTION (BY CHAIN RULE )
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  2. Derivative of sqrt( tan sqrt(x)) with respect to x is

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

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