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If for x (0,1/4), the derivative of tan^...

If for `x (0,1/4),` the derivative of `tan^(-1)((6xsqrt(x))/(1-9x^3))` is `sqrt(x)dotg(x),` then `g(x)` equals: `(3x)/(1-9x^3)` (2) `3/(1+9x^3)` (3) `9/(1+9x^3)` (4) `(3xsqrt(x))/(1-9x^3)`

A

`1//2`

B

1

C

`sqrt(2)`

D

`1sqrt(2)`

Text Solution

AI Generated Solution

To find \( g(x) \) such that the derivative of \( \tan^{-1}\left(\frac{6x\sqrt{x}}{1-9x^3}\right) \) equals \( \sqrt{x} g(x) \), we will differentiate the function step by step. ### Step 1: Define the function Let \[ y = \tan^{-1}\left(\frac{6x\sqrt{x}}{1-9x^3}\right) \] ...
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