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d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))] ...

`d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))] is `
(a) `1/(2(1+x)sqrt(x))` (b) `3/((1+x)sqrt(x))` (c) `2/((1+x)sqrt(x))` (d) `3/(2(1+x)sqrt(x))`

A

`(1)/(2(1+x)sqrt(x))`

B

`(3)/((1+x)sqrt(x))`

C

`(2)/((1+x)sqrt(x))`

D

`(3)/(2(1+x)sqrt(x))`

Text Solution

Verified by Experts

`(d)/(dx)(tan^(-1)""(sqrt(x)(3-x))/(1-3x))`
`(d)/(dx)(tan^(-1)""((tan theta(3-tan^(2)theta)))/(1-3tan^(2)theta))`
`("putting "sqrt(x)=tan theta or theta=tan^(-1)sqrt(x))`
`=(d)/(dx)(tan^(-1)""((3tantheta-tan^(3)theta))/(1-3tan^(2)theta))`
`=(d)/(dx)[tan^(-1)(tan 3theta)]=(d)/(dx)(3theta)`
`=(d)/(dx)[3tan^(-1)sqrt(x)]=(3)/(2sqrt(x)(1+x))`
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