Question

यदि (If) `y=logsqrt((1+sin^(2)x)/(1-tanx))`, (find) `(dy)/(dx)` ज्ञात करें ।

Answer 1

`y=logsqrt((1+sin^(2)x)/(1-tanx))=(1)/(2)log((1+sin^(2)x)/(1-tanx))`
`=(1)/(2)[log(1+sin^(2)x)-log(1-tanx)]`
`rArr(dy)/(dx)=(1)/(2)[(1)/(1+sin^(2)x)*(d)/(dx)(1+sin^(2)x)-(1)/(1-tanx)*(d)/(dx)(1-tanx)]`
`=(1)/(2)[(sin2x)/(1+sin^(2)x)+(sec^(2)x)/(1-tanx)]`