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Question
Find `dy/dx` if `y = tan^(-1) ((5x+ 1)/(3-x-6x^2))`
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Solution
Let `y = tan^(-1) ((5x+ 1)/(3-x-6x^2))`
`= tan^(-1) ((5x+1)/(1+2-x-6x^2))`
`= tan^(-1) ((5x+ 1)/(1-(3x + 2)(2x-11)))`
`= tan^(-1) (((3x+2)+(2x-1))/((1-(3x+2))(2x-1)))`
`y = tan^(-1)(3x + 2) + tan^(-1) (2x - 1)`
Differentiate w.r.t. x
`:. dy/dx = 3/(1+(3x+2)^2) + 2/(1+(2x-1)^2)`
`= 3/(1+9x^2+12x+ 4)+ 2/(1+4x^2-4x +1)`
`= 3/(9x^2+12x+5) + 1/(2x^2-2x+1)`
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