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Solution - find dy/dx if y=tan^−1 (6x/(1−5x^2)) - Derivative - Derivative of Inverse Function

Question

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

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)`

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APPEARS IN

2014-2015 (March)
Question 2.1.3 | 3 marks
Solution for question: find dy/dx if y=tan^−1 (6x/(1−5x^2)) concept: Derivative - Derivative of Inverse Function. For the courses HSC Arts, HSC Commerce, HSC Commerce (Marketing and Salesmanship), HSC Science (Computer Science), HSC Science (Electronics), HSC Science (General)
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