Find the Derivative of the following function

f(x)=1/ln((x^2)+2)

### 1 Answer | Add Yours

Since the function is a fraction you need to differentiate using the quotient rule. Notice that the denominator is a composed function. You need to differentiate the denominator using the chain rule.

Using the quotient rule yields:`f'(x) = ((1)'*(ln (x^2+2)) - 1*(ln (x^2+2))')/(ln^2 (x^2+2))`

Using the chain rule yields:`(ln (x^2+2))' = (1/(x^2+2))*(x^2+2)'=gt`

`` `(ln (x^2+2))' = (2x)/(x^2+2)`

`f'(x) = (0 - (2x)/(x^2+2))/(ln^2 (x^2+2))`

`f'(x) = (2x)/((x^2+2)*(ln^2 (x^2+2)))`

**Computing the derivative of the function `f(x)=1/(ln (x^2+2)) ` yields **

**`f'(x) = (2x)/((x^2+2)*(ln^2 (x^2+2))).` **

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes