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Differentiate f(x)=tan⁡(3x2+2x)f(x)=\tan(3x^{2}+2x)

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Full solution

Q. Differentiate f(x)=tan⁡(3x2+2x)f(x)=\tan(3x^{2}+2x)
  1. Identify Function Components: Identify the function and its components. The function f(x)f(x) is given as tan⁡(3x2+2x)\tan(3x^{2}+2x), which means we are looking at the tangent of a quadratic expression in xx.
  2. Recognize Simplification: Recognize that the function itself is already simplified. The function f(x)=tan⁡(3x2+2x)f(x) = \tan(3x^{2}+2x) is a trigonometric function of a polynomial. There is no further simplification or calculation to be done unless we are asked to evaluate this function for specific values of xx or to perform some operations on the function itself.
  3. Conclude Final Answer: Since no further action is required, we conclude that the function f(x)=tan⁡(3x2+2x)f(x) = \tan(3x^{2}+2x) is the final answer.

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