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Find (dy)/(dx) if y=tan^(-1)(4x)/(1+5x^2...

Find `(dy)/(dx)` if `y=tan^(-1)(4x)/(1+5x^2)+tan^(-1)(2+3x)/(3-2x)`

Text Solution

Verified by Experts

The correct Answer is:
`(5)/(1+25 x^(2))`
`y=tan^(-1)""(4x)/(1+5x^(2))+tan^(-1)""(2+3x)/(3-2x)`
`=tan^(-1)""(5x-x)/(1+5xcdotx)+tan^(-1)""((2)/(3)+x)/(1-(2)/(3)x)`
`tan^(-1)5x-tan^(-1)x +tan^(-1)""(2)/(3)+tan^(-1)x`
`=tan^(-1)""5x+tan^(-1)""(2)/(3)`
`therefore" "(dy)/(dx)=(5)/(1+25x^(2))`
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