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find dy/dx if y=tan^−1 (6x/(1−5x^2)) - Mathematics and Statistics

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find dy/dx if `y=tan^-1((6x)/(1-5x^2))`

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Solution

Let ` y=tan^-1((6x)/(1-5x^2))`

`=tan^-1((x+5x)/(1-5x^2))`

`y=tan^-1(x)+tan^-1(5x)`

Differentiating w.r.t x

`dy/dx=1/(1+x^2)+1/(1+25x^2)xx5`

`=1/(1+x^2)+5/(1+25x^2)`

Concept: The Concept of Derivative - Derivative of Inverse Function
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