009A Sample Final 1, Problem 4

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If   compute    and find the equation for the tangent line at  

You may leave your answers in point-slope form.

1. Chain Rule
2. Recall
3. The equation of the tangent line to    at the point    is


Step 1:  
First, we compute  
Using the Chain Rule, we get


Step 2:  
To find the equation of the tangent line, we first find the slope of the line.
Using    in the formula for    from Step 1, we get


Step 3:  
To get a point on the line, we plug in    into the equation given.
So, we have


Thus, the equation of the tangent line is  

Final Answer:  



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