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

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

Discussion

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