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Question
Differentiate `tan^-1((8x)/(1 - 15x^2))` w.r. to x
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
`("d"y)/("d"x) = "d"/("d"x)(tan^-1 5x + tan^-1 3x)`
= `1/(1 + (5x)^2)*"d"/("d"x)(5x) + 1/(1 + (3x)^2)*"d"/("d"x)(3x)`
= `1/(1 + 25x^2)*(5) + 1/(1 + 9x^2)*3`
∴ `("d"y)/("d"x) = 5/(1 + 25x^2) + 3/(1 + 9x^2)`
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