Question

Find an equation of the tangent line to the graph of the function at the given point.

Answer 1

Step 1 :

The function is and the point is .

The slope of the tangent line is equal to the derivative of the given function at .

Rewrite the function as :

Apply power rule of natural logarithm : .

Apply formula : .

Differentiate the function with respect to . 

Apply formula : .

Apply product rule of derivatives : .

Apply formula : .

Step 2 :

Slope at the point :

Substitute the point in .

Slope .

Step 3 :

Point-slope form of a line equation .

Substitute point and in the above equation. 

The tangent line equation is .

Solution :

The tangent line equation is .