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Question
Differentiate the following w.r.t. x : `tan^-1((8x)/(1 - 15x^2))`
Solution
Let y = `tan^-1((8x)/(1 - 15x^2))`
= `tan^-1[(5x + 3x)/(1 - (5x)(3x))]`
= tan–1(5x) + tan–1(3x)
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"[tan^-1(5x) + tan^-1(3x)]`
= `"d"/"dx"[tan^-1(5x)] + "d"/"dx"[tan^-1(3x)]`
= `(1)/(1 + (5x)^2)."d"/"dx"(5x) + (1)/(1 + (3x)^2)."d"/"dx"(3x)`
= `(1)/(1 + 25x^2) xx 5 + (1)/(1 + 9x^2) xx 3`
= `(5)/(1 + 25x^2) + (3)/(1 + 9x^2)`.
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