# Solution assignment 05 Implicit differentiation

### 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.