Find an equation of the tangent line

Question

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

f(x)=ln(9(x+4)/x ; (-9/2, 0)

y=

Answer 1

Using the Laws of Logs:

y=ln(9)+ln(x+4)-ln(x)

y'=1/(x+4)-1/x

Subbing in x=-9/2 we obtain

y'=-19/9 (Fraction arithmetic)

So the final equation in POINT SLOPE form would be

y=-19/9(x+9/2)

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