`y = 2x - (x^2)tan(x)` Use the Product Rule or the Quotient Rule to find the derivative of the function.

Textbook Question

Chapter 2, Review - Problem 38 - Calculus of a Single Variable (10th Edition, Ron Larson).
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gsarora17 | (Level 2) Associate Educator

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`y=2x-x^2tan(x)`

Now to evaluate the derivative , let us first apply the Sum/Difference rule i.e.

`(f+-g)'=f'+-g'`

`y'=d/dx(2x)-d/dx(x^2tan(x))`

`y'=2-d/dx(x^2tan(x))`

Now applying the product rule for evaluating the derivative of `x^2tan(x) ,`

`y'=2-(x^2d/dx(tan(x))+tan(x)d/dx(x^2))`

`y'=2-(x^2sec^2(x)+tan(x)*(2x))`

`y'=2-x^2sec^2(x)-2xtan(x)`

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