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Find (dy)/(dx) for the function: y=sin^(...

Find `(dy)/(dx)` for the function: `y=sin^(-1)sqrt((1-x))+cos^(-1)sqrt(x)`

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Verified by Experts

The correct Answer is:
`(-1)/(sqrt(x-x^(2)))`
`sin^(-1)sqrt(1-x)=sin^(-1)sqrt(1(sqrt(x))^(2))=cos^(-1)sqrt(x)`
`therefore" "y=2 cos^(-1)sqrt(x)`
`"or "(dy)/(dx)=2xx(-1)/(sqrt(1-x))xx(1)/(2sqrt(xx))=(-1)/(sqrt(1-x^(2))`
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CENGAGE-DIFFERENTIATION-Exercise 3.2
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  7. y=tan^(-1)(x/(1+sqrt(1-x^2)))

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  8. Find (dy)/(dx) for the function: y=sin^(-1)sqrt((1-x))+cos^(-1)sqrt(x)

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  9. Find (dy)/(dx) for the function: y=sqrt(sinsqrt(x))

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  10. Differentiate : y = e^(sin 2x)

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  11. Find (dy)/(dx) for the function: y=logsqrt(sinsqrt(e^x))

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  12. Find (dy)/(dx) for the function: y=a^((sin^(-1)x))^2

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  16. Find (dy)/(dx) for the function: y=(log)esqrt((1+sinx)/(1-sinx)),w h e...

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  20. If g is the inverse function of fa n df^(prime)(x)=sinx ,t h e ng^(pri...

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