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Find (dy)/(dx) " when " y = sin^(-1) ...

Find ` (dy)/(dx) " when " y = sin^(-1) sqrt((1+x^(2))/2)`

Text Solution

Verified by Experts

The correct Answer is:
`x/(sqrt(1-x^(4))`
Let `x^(2) = cos theta Rightarrow theta = cos^(-1) x^(2)`
` y = sin^(-1) sqrt((1+ cos theta)/2)`
`y = sin^(-1) (cos ""theta/2) = sin^(-1) (sin (pi/2 - theta/2))`
` = pi/2 - theta/2 = pi/2 - 1/2 "" cos ^(-1) x^(2)`
` Rightarrow (dy)/(dx) = 1/(2sqrt(1-x^(4))) (2x)`
` (dy)/(dx) = x/(sqrt(1-x^(4)))`
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