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### Assignment 5

Calculate the tangent line at the point of the following graph:

### Solution

First we have to verify that the point lies on the graph, and yes, we have:

Next we have to determine the derivative and use both the product and quotient rule:

and thus:

and thus in the point :

The equation of the tangent line becomes:

or .

Also in this case implicit differentiation is not necessary. We can write the function in explicit form quite easily:

and thus, after applying the logarithm in the left- and right-hand side we get:

Differentiation of this function gives the result found above.

Return to Assignments Implicit differentiation