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Given f(x)=2tan(x), find f^(')(x). Answer: f^(')(x)=

Given f(x)=2tan⁡(x) f(x)=2 \tan (x) , find f′(x) f^{\prime}(x) .\newlineAnswer: f′(x)= f^{\prime}(x)=

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Q. Given f(x)=2tan⁡(x) f(x)=2 \tan (x) , find f′(x) f^{\prime}(x) .\newlineAnswer: f′(x)= f^{\prime}(x)=
  1. Identify Function: Identify the function to differentiate.\newlineWe are given the function f(x)=2tan⁡(x)f(x) = 2\tan(x) and we need to find its derivative, which is denoted by f′(x)f^{\prime}(x).
  2. Apply Rule: Apply the derivative rule for the tangent function.\newlineThe derivative of tan⁡(x)\tan(x) with respect to xx is sec⁡2(x)\sec^2(x). Therefore, the derivative of 2tan⁡(x)2\tan(x) is 22 times the derivative of tan⁡(x)\tan(x).
  3. Calculate Derivative: Calculate the derivative.\newlineUsing the rule from Step 22, we find that f′(x)=2⋅sec⁡2(x)f'(x) = 2 \cdot \sec^2(x).

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