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Find the derivative of the trigonometric function f(x) = x² * tan x.

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Final answer:

To find the derivative of the trigonometric function f(x)=x² * tan(x), use the product rule. The derivative is (2x * tan(x)) + (x² * sec²(x)).

Step-by-step explanation:

To find the derivative of the trigonometric function f(x)=x² * tan(x), we can use the product rule. The product rule states that if we have two functions, u(x) and v(x), then the derivative of their product is given by the formula (u(x) * v'(x)) + (u'(x) * v(x)). In this case, u(x) = x² and v(x) = tan(x).

Using the product rule, we can find that the derivative of f(x) is f'(x) = (2x * tan(x)) + (x² * sec²(x)). So, the derivative of f(x) is (2x * tan(x)) + (x² * sec²(x)).

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