Answer:-
The derivative of tan(x) with respect to x is sec²(x). In calculus, this is a standard derivative result that comes from applying the quotient rule or from knowing basic trigonometric derivatives. Since tan(x) = sin(x)/cos(x), differentiating it involves applying the quotient rule, which gives (cos²(x) + sin²(x)) / cos²(x), simplifying to 1/cos²(x) or sec²(x). This derivative is valid for all values of x where cos(x) ≠ 0, meaning the function is undefined at odd multiples of π/2. This result is especially useful in solving calculus problems involving trigonometric functions.
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