Find the Derivative of the following function f(x)=1/ln((x^2)+2)

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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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))).`