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

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

Text Solution

Verified by Experts

The correct Answer is:
`(2log a sin^(-1)x)/(sqrt(1-x^(2)))a(sin^(-1)x)^(2)`
`"Let "y=a^((sin^(-1)x)^(2))`.
Using chain rule, we get
`(dy)/(dx)=(d)/(dx){a^((sin^(-1)x)^(2))}`
`=a^((sin^(-1)x)^(2))loga(d)/(x){(sin^(-1)x)^(2)}`
`=a^((sin^(-1)x)^(2))(log a) 2 (sin ^(-1)x)^(1)(d)/(dx)(sin^(-1)x)`
`=a^((sin^(-1)x)^(2))(log a)2 sin^(-1)x(1)/(sqrt(1-x^(2)))`
`=(2 log a sin^(-1)x)/(sqrt(1-x^(2)))a^((sin^(-1)x)^(2))`
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