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Given , write the equation of the line tangent to when

Ask by Salazar Lane. in the United States
Jan 25,2025

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The equation of the tangent line to at is:

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To find the equation of the tangent line to at , we first need to calculate and then find the derivative .
  1. Calculate :
    Since ,
  2. Find :
    Using the chain rule,
    Now, we need to evaluate :
    Knowing ,
    Therefore,
  3. Now we have the point and the slope . The equation of the tangent line in point-slope form is:
    Simplifying gives:
    Rearranging gives the tangent line’s equation:
Thus, the equation of the tangent line is:

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